Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.56 * 8.314 * 565 / 101.9.
Final: {"answer": 118.0115, "unit": "kPa"}

Answer: 118.0115

Prompt: An ideal gas sample has n=2.56 mol, T=565 K, and V=101.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.56 * 8.314 * 565 / 101.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1900 * 2.72 * 46.
Final: {"answer": 237728.0, "unit": "J"}

Answer: 237728.0

Prompt: A 1900 g sample has specific heat 2.72 J/(g*K). How much heat is needed to raise its temperature by 46 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1900 * 2.72 * 46.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=25.2 V and R=88.2 ohm.
Final: {"answer": 7.2, "unit": "W"}

Answer: 7.2

Prompt: A resistor has resistance 88.2 ohm and voltage 25.2 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=25.2 V and R=88.2 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=627 mg, t=44 h, and T_half=45.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 320.7463, "unit": "mg"}

Answer: 320.7463

Prompt: A radioactive sample starts with 627 mg. Its half-life is 45.5 hours. How many mg remain after 44 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=627 mg, t=44 h, and T_half=45.5 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.92 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 260.5392, "unit": "g"}

Answer: 260.5392

Prompt: A sample contains 5.92 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.92 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 315 mL to 0.315 L.
3. Compute M = 4.165 / 0.315.
Final: {"answer": 13.2222, "unit": "mol/L"}

Answer: 13.2222

Prompt: A solution contains 4.165 mol of solute in 315 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 315 mL to 0.315 L.
Compute M = 4.165 / 0.315.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 0.0022, "unit": "state_units"}

Answer: 0.0022

Prompt: Use explicit Euler on dy/dt = -0.85 y with y(0)=21, step size h=1.55, for 8 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.
Apply that update for 8 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-9.7)=-49.16 and f(-4.4)=-29.02.
3. The interval width is 5.3.
Final: {"answer": -207.177, "unit": "area_units"}

Answer: -207.177

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.8x+-12.3 from x=-9.7 to x=-4.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.7)=-49.16 and f(-4.4)=-29.02.
The interval width is 5.3.

(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.46 and add it to the current value.
Final: {"answer": [-1.45, 1.175, -0.3], "unit": "temperature_units"}

Answer: -1.45

Answer: 1.175

Answer: -0.3

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.8, right=0.9; current interior values are [2.0, -1.7, 0.85]. Use r=0.46. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.46 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 2086.5 / 100.
Final: {"answer": 20.865, "unit": "m"}

Answer: 20.865

Prompt: Convert 2086.5 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 2086.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=71 degrees and keep the unit as newtons.
Final: {"answer": [34.9986, 101.6432], "unit": "N"}

Answer: 34.9986

Answer: 101.6432

Prompt: A vector has magnitude 107.5 N at 71 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=71 degrees and keep the unit as newtons.

[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. energy divided by length is force, not spring constant
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In sensor calibration case 680133, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
energy divided by length is force, not spring constant
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: left_boundary, right_boundary.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.08 and interior values [-1.3, 2.55, -0.45], but gives no boundary values. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: left_boundary, right_boundary.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 23.55^2 and multiply by 0.5 * 15.95.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 4422.9549, "unit": "J"}

Answer: 4422.9549

Prompt: A body of mass 15.95 kg moves at 23.55 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 23.55^2 and multiply by 0.5 * 15.95.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=24 degrees through the sine of 2 theta.
3. Substitute v=56.1 m/s and g=9.81 m/s^2.
Final: {"answer": 238.4131, "unit": "m"}

Answer: 238.4131

Prompt: A projectile is launched on level ground with no air resistance at speed 56.1 m/s and angle 24 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=24 degrees through the sine of 2 theta.
Substitute v=56.1 m/s and g=9.81 m/s^2.

speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.05 * 8.314 * 509 / 74.8.
Final: {"answer": 285.7048, "unit": "kPa"}

Answer: 285.7048

Prompt: An ideal gas sample has n=5.05 mol, T=509 K, and V=74.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.05 * 8.314 * 509 / 74.8.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=51.6 V and R=78.4 ohm.
Final: {"answer": 33.9612, "unit": "W"}

Answer: 33.9612

Prompt: A resistor has resistance 78.4 ohm and voltage 51.6 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=51.6 V and R=78.4 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.29 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 192.2676, "unit": "g"}

Answer: 192.2676

Prompt: A sample contains 3.29 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 3.29 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.01 y, so each step multiplies y by 1 - h*0.01.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 42.9333, "unit": "state_units"}

Answer: 42.9333

Prompt: Use explicit Euler on dy/dt = -0.01 y with y(0)=44, step size h=0.35, for 7 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.01 y, so each step multiplies y by 1 - h*0.01.
Apply that update for 7 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6.5)=49.9 and f(0.6)=8.72.
3. The interval width is 7.1.
Final: {"answer": 208.101, "unit": "area_units"}

Answer: 208.101

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.8x+12.2 from x=-6.5 to x=0.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.5)=49.9 and f(0.6)=8.72.
The interval width is 7.1.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.46 and add it to the current value.
Final: {"answer": [0.386, 0.225, 2.294], "unit": "temperature_units"}

Answer: 0.386

Answer: 0.225

Answer: 2.294

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.05, right=2.95; current interior values are [-0.35, 1.95, 0.5]. Use r=0.46. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.46 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4547.0 / 100.
Final: {"answer": 45.47, "unit": "m"}

Answer: 45.47

Prompt: Convert 4547 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 4547.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=56 degrees and keep the unit as newtons.
Final: {"answer": [75.491, 111.9201], "unit": "N"}

Answer: 75.491

Answer: 111.9201

Prompt: A vector has magnitude 135 N at 56 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=56 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-2.05, -25.75], "unit": "dimensionless"}

Answer: -2.05

Answer: -25.75

Prompt: A line passes through points (-10.75, -3.7125) and (-6.5, -12.425). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. mass times acceleration has newton dimensions
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In student derivation case 472590, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
mass times acceleration has newton dimensions
The equation is valid only if both sides have identical dimensions.

Answer: consistent


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def finite_differences_000484(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_000484"}

Answer: python_code

Prompt: Write a Python function finite_differences_000484(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.

assert finite_differences_000484([5]) == []

assert finite_differences_000484([]) == []


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: target_schema, valid_examples.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each mobile invoice record from batch 246070 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: target_schema, valid_examples.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 10.5 kg and a = 12.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 131.25, "unit": "N"}

Answer: 131.25

Prompt: A cart has mass 10.5 kg and measured acceleration 12.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 10.5 kg and a = 12.5 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 5.65^2 and multiply by 0.5 * 27.4.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 437.3383, "unit": "J"}

Answer: 437.3383

Prompt: A body of mass 27.4 kg moves at 5.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 5.65^2 and multiply by 0.5 * 27.4.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=39 degrees through the sine of 2 theta.
3. Substitute v=24.7 m/s and g=9.81 m/s^2.
Final: {"answer": 60.8316, "unit": "m"}

Answer: 60.8316

Prompt: A projectile is launched on level ground with no air resistance at speed 24.7 m/s and angle 39 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=39 degrees through the sine of 2 theta.
Substitute v=24.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.16 * 8.314 * 585 / 38.3.
Final: {"answer": 147.3076, "unit": "kPa"}

Answer: 147.3076

Prompt: An ideal gas sample has n=1.16 mol, T=585 K, and V=38.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.16 * 8.314 * 585 / 38.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 380 * 4.035 * 91.
Final: {"answer": 139530.3, "unit": "J"}

Answer: 139530.3

Prompt: A 380 g sample has specific heat 4.035 J/(g*K). How much heat is needed to raise its temperature by 91 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 380 * 4.035 * 91.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=66.8 V and R=95.8 ohm.
Final: {"answer": 46.5787, "unit": "W"}

Answer: 46.5787

Prompt: A resistor has resistance 95.8 ohm and voltage 66.8 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=66.8 V and R=95.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=680.5 mg, t=46 h, and T_half=30.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 239.23, "unit": "mg"}

Answer: 239.23

Prompt: A radioactive sample starts with 680.5 mg. Its half-life is 30.5 hours. How many mg remain after 46 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=680.5 mg, t=46 h, and T_half=30.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.56 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 441.8064, "unit": "g"}

Answer: 441.8064

Prompt: A sample contains 7.56 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.56 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4610 mL to 4.61 L.
3. Compute M = 3.805 / 4.61.
Final: {"answer": 0.8254, "unit": "mol/L"}

Answer: 0.8254

Prompt: A solution contains 3.805 mol of solute in 4610 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4610 mL to 4.61 L.
Compute M = 3.805 / 4.61.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 18.3283, "unit": "state_units"}

Answer: 18.3283

Prompt: Use explicit Euler on dy/dt = -0.41 y with y(0)=23.5, step size h=0.05, for 12 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.
Apply that update for 12 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.38 and add it to the current value.
Final: {"answer": [-0.182, 0.406, 0.647], "unit": "temperature_units"}

Answer: -0.182

Answer: 0.406

Answer: 0.647

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.3, right=2.45; current interior values are [1.3, -1.0, 0.4]. Use r=0.38. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.38 and add it to the current value.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 242.0 + 273.15.
Final: {"answer": 515.15, "unit": "K"}

Answer: 515.15

Prompt: Convert 242 degC to K. Return the converted value with unit.

Kelvin equals Celsius plus 273.15.
Apply the conversion factor directly to the given value.
Compute 242.0 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=114 degrees and keep the unit as newtons.
Final: {"answer": [-110.0223, 247.114], "unit": "N"}

Answer: -110.0223

Answer: 247.114

Prompt: A vector has magnitude 270.5 N at 114 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=114 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [6.3, -27.0], "unit": "dimensionless"}

Answer: 6.3

Answer: -27.0

Prompt: A line passes through points (10.75, 40.725) and (25.75, 135.225). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. lever arm times force has torque dimensions
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In simulation spec case 183617, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
lever arm times force has torque dimensions
The equation is valid only if both sides have identical dimensions.

Answer: consistent


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def weighted_sum_000502(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_000502"}

Answer: python_code

Prompt: Write a Python function weighted_sum_000502(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.

try:
    weighted_sum_000502([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: volume.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=1.39 mol and T=562 K, but does not give volume. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: volume.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=27 degrees through the sine of 2 theta.
3. Substitute v=51.1 m/s and g=9.81 m/s^2.
Final: {"answer": 215.3428, "unit": "m"}

Answer: 215.3428

Prompt: A projectile is launched on level ground with no air resistance at speed 51.1 m/s and angle 27 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=27 degrees through the sine of 2 theta.
Substitute v=51.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.71 * 8.314 * 440 / 76.9.
Final: {"answer": 176.486, "unit": "kPa"}

Answer: 176.486

Prompt: An ideal gas sample has n=3.71 mol, T=440 K, and V=76.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.71 * 8.314 * 440 / 76.9.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=15.8 V and R=190.8 ohm.
Final: {"answer": 1.3084, "unit": "W"}

Answer: 1.3084

Prompt: A resistor has resistance 190.8 ohm and voltage 15.8 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=15.8 V and R=190.8 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.46 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 263.0278, "unit": "g"}

Answer: 263.0278

Prompt: A sample contains 1.46 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.46 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2235 mL to 2.235 L.
3. Compute M = 0.605 / 2.235.
Final: {"answer": 0.2707, "unit": "mol/L"}

Answer: 0.2707

Prompt: A solution contains 0.605 mol of solute in 2235 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2235 mL to 2.235 L.
Compute M = 0.605 / 2.235.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.19 y, so each step multiplies y by 1 - h*0.19.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 52.8725, "unit": "state_units"}

Answer: 52.8725

Prompt: Use explicit Euler on dy/dt = -0.19 y with y(0)=78.5, step size h=0.4, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.19 y, so each step multiplies y by 1 - h*0.19.
Apply that update for 5 steps and round the final state.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 36983.0 / 1000.
Final: {"answer": 36.983, "unit": "kg"}

Answer: 36.983

Prompt: Convert 36983 g to kg. Return the converted value with unit.

There are 1000 grams in one kilogram.
Apply the conversion factor directly to the given value.
Compute 36983.0 / 1000.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-9.3, -18.0], "unit": "dimensionless"}

Answer: -9.3

Answer: -18.0

Prompt: A line passes through points (-15, 121.5) and (-4, 19.2). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. m*v is momentum, not energy
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In model card equation case 585139, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
m*v is momentum, not energy
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def center_values_000520(values):
    if not values:
        raise ValueError('center_values requires at least one value')
    mean = sum(values) / len(values)
    return [value - mean for value in values]
```
Final: {"answer": "python_code", "function": "center_values_000520"}

Answer: python_code

Prompt: Write a Python function center_values_000520(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.

try:
    center_values_000520([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: volume.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=4.06 mol and T=594 K, but does not give volume. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: volume.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 23.65 kg and a = 14.7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 347.655, "unit": "N"}

Answer: 347.655

Prompt: A cart has mass 23.65 kg and measured acceleration 14.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 23.65 kg and a = 14.7 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=17 degrees through the sine of 2 theta.
3. Substitute v=20.6 m/s and g=9.81 m/s^2.
Final: {"answer": 24.1895, "unit": "m"}

Answer: 24.1895

Prompt: A projectile is launched on level ground with no air resistance at speed 20.6 m/s and angle 17 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=17 degrees through the sine of 2 theta.
Substitute v=20.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.71 * 8.314 * 327 / 72.8.
Final: {"answer": 138.548, "unit": "kPa"}

Answer: 138.548

Prompt: An ideal gas sample has n=3.71 mol, T=327 K, and V=72.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.71 * 8.314 * 327 / 72.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1765 * 2.22 * 20.
Final: {"answer": 78366.0, "unit": "J"}

Answer: 78366.0

Prompt: A 1765 g sample has specific heat 2.22 J/(g*K). How much heat is needed to raise its temperature by 20 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1765 * 2.22 * 20.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=109 V and R=128.1 ohm.
Final: {"answer": 92.7479, "unit": "W"}

Answer: 92.7479

Prompt: A resistor has resistance 128.1 ohm and voltage 109 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=109 V and R=128.1 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.35 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 783.6786, "unit": "g"}

Answer: 783.6786

Prompt: A sample contains 4.35 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.35 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1220 mL to 1.22 L.
3. Compute M = 2.53 / 1.22.
Final: {"answer": 2.0738, "unit": "mol/L"}

Answer: 2.0738

Prompt: A solution contains 2.53 mol of solute in 1220 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1220 mL to 1.22 L.
Compute M = 2.53 / 1.22.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 3.1073, "unit": "state_units"}

Answer: 3.1073

Prompt: Use explicit Euler on dy/dt = -0.41 y with y(0)=24, step size h=0.55, for 8 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.
Apply that update for 8 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6.1)=6.55 and f(3.1)=-7.25.
3. The interval width is 9.2.
Final: {"answer": -3.22, "unit": "area_units"}

Answer: -3.22

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.5x+-2.6 from x=-6.1 to x=3.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.1)=6.55 and f(3.1)=-7.25.
The interval width is 9.2.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 191.5 + 273.15.
Final: {"answer": 464.65, "unit": "K"}

Answer: 464.65

Prompt: Convert 191.5 degC to K. Return the converted value with unit.

Kelvin equals Celsius plus 273.15.
Apply the conversion factor directly to the given value.
Compute 191.5 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=326 degrees and keep the unit as newtons.
Final: {"answer": [39.3793, -26.5617], "unit": "N"}

Answer: 39.3793

Answer: -26.5617

Prompt: A vector has magnitude 47.5 N at 326 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=326 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [5.85, -2.25], "unit": "dimensionless"}

Answer: 5.85

Answer: -2.25

Prompt: A line passes through points (-1.75, -12.4875) and (4.25, 22.6125). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. coulomb per second is ampere
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In sensor calibration case 821933, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
coulomb per second is ampere
The equation is valid only if both sides have identical dimensions.

Answer: consistent


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: launch_angle_or_vertical_velocity.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 71.6 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: launch_angle_or_vertical_velocity.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 4.75 kg and a = 13.7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 65.075, "unit": "N"}

Answer: 65.075

Prompt: A cart has mass 4.75 kg and measured acceleration 13.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 4.75 kg and a = 13.7 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 30.9^2 and multiply by 0.5 * 8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3819.24, "unit": "J"}

Answer: 3819.24

Prompt: A body of mass 8 kg moves at 30.9 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 30.9^2 and multiply by 0.5 * 8.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=79 degrees through the sine of 2 theta.
3. Substitute v=70.8 m/s and g=9.81 m/s^2.
Final: {"answer": 191.4137, "unit": "m"}

Answer: 191.4137

Prompt: A projectile is launched on level ground with no air resistance at speed 70.8 m/s and angle 79 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=79 degrees through the sine of 2 theta.
Substitute v=70.8 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1025 * 4.785 * 63.
Final: {"answer": 308991.375, "unit": "J"}

Answer: 308991.375

Prompt: A 1025 g sample has specific heat 4.785 J/(g*K). How much heat is needed to raise its temperature by 63 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1025 * 4.785 * 63.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=289 mg, t=238.5 h, and T_half=30 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 1.1687, "unit": "mg"}

Answer: 1.1687

Prompt: A radioactive sample starts with 289 mg. Its half-life is 30 hours. How many mg remain after 238.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=289 mg, t=238.5 h, and T_half=30 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3545 mL to 3.545 L.
3. Compute M = 1.35 / 3.545.
Final: {"answer": 0.3808, "unit": "mol/L"}

Answer: 0.3808

Prompt: A solution contains 1.35 mol of solute in 3545 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3545 mL to 3.545 L.
Compute M = 1.35 / 3.545.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.14 y, so each step multiplies y by 1 - h*0.14.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 2.6963, "unit": "state_units"}

Answer: 2.6963

Prompt: Use explicit Euler on dy/dt = -0.14 y with y(0)=15.5, step size h=1.05, for 11 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.14 y, so each step multiplies y by 1 - h*0.14.
Apply that update for 11 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(1.3)=-1.49 and f(7.3)=8.71.
3. The interval width is 6.
Final: {"answer": 21.66, "unit": "area_units"}

Answer: 21.66

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.7x+-3.7 from x=1.3 to x=7.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.3)=-1.49 and f(7.3)=8.71.
The interval width is 6.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.34 and add it to the current value.
Final: {"answer": [1.079, 1.137, 1.335], "unit": "temperature_units"}

Answer: 1.079

Answer: 1.137

Answer: 1.335

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.1, right=0.9; current interior values are [0.45, 2.65, 0.4]. Use r=0.34. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.34 and add it to the current value.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -42.5 + 273.15.
Final: {"answer": 230.65, "unit": "K"}

Answer: 230.65

Prompt: Convert -42.5 degC to K. Return the converted value with unit.

Kelvin equals Celsius plus 273.15.
Apply the conversion factor directly to the given value.
Compute -42.5 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=258 degrees and keep the unit as newtons.
Final: {"answer": [-17.9844, -84.6098], "unit": "N"}

Answer: -17.9844

Answer: -84.6098

Prompt: A vector has magnitude 86.5 N at 258 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=258 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [4.65, 10.25], "unit": "dimensionless"}

Answer: 4.65

Answer: 10.25

Prompt: A line passes through points (18.75, 97.4375) and (27.75, 139.288). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. amount times volume is not concentration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In student derivation case 15775, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
amount times volume is not concentration
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: rate_constant, number_of_steps.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=37 and h=0.15, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: rate_constant, number_of_steps.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 8.8 kg and a = 13.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 118.36, "unit": "N"}

Answer: 118.36

Prompt: A cart has mass 8.8 kg and measured acceleration 13.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 8.8 kg and a = 13.45 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 6.15^2 and multiply by 0.5 * 21.25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 401.8641, "unit": "J"}

Answer: 401.8641

Prompt: A body of mass 21.25 kg moves at 6.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 6.15^2 and multiply by 0.5 * 21.25.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=75 degrees through the sine of 2 theta.
3. Substitute v=60.5 m/s and g=9.81 m/s^2.
Final: {"answer": 186.5571, "unit": "m"}

Answer: 186.5571

Prompt: A projectile is launched on level ground with no air resistance at speed 60.5 m/s and angle 75 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=75 degrees through the sine of 2 theta.
Substitute v=60.5 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.45 * 8.314 * 485 / 20.7.
Final: {"answer": 282.4551, "unit": "kPa"}

Answer: 282.4551

Prompt: An ideal gas sample has n=1.45 mol, T=485 K, and V=20.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.45 * 8.314 * 485 / 20.7.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=207.9 V and R=98.3 ohm.
Final: {"answer": 439.699, "unit": "W"}

Answer: 439.699

Prompt: A resistor has resistance 98.3 ohm and voltage 207.9 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=207.9 V and R=98.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=981 mg, t=19.5 h, and T_half=34.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 663.0124, "unit": "mg"}

Answer: 663.0124

Prompt: A radioactive sample starts with 981 mg. Its half-life is 34.5 hours. How many mg remain after 19.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=981 mg, t=19.5 h, and T_half=34.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1470 mL to 1.47 L.
3. Compute M = 3.2 / 1.47.
Final: {"answer": 2.1769, "unit": "mol/L"}

Answer: 2.1769

Prompt: A solution contains 3.2 mol of solute in 1470 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1470 mL to 1.47 L.
Compute M = 3.2 / 1.47.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.0002, "unit": "state_units"}

Answer: 0.0002

Prompt: Use explicit Euler on dy/dt = -0.58 y with y(0)=6.5, step size h=1, for 12 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.
Apply that update for 12 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-2.5)=-13.8 and f(4)=-13.8.
3. The interval width is 6.5.
Final: {"answer": -89.7, "unit": "area_units"}

Answer: -89.7

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0x+-13.8 from x=-2.5 to x=4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-2.5)=-13.8 and f(4)=-13.8.
The interval width is 6.5.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.3 and add it to the current value.
Final: {"answer": [1.075, 0.595, 0.055], "unit": "temperature_units"}

Answer: 1.075

Answer: 0.595

Answer: 0.055

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.9, right=-0.9; current interior values are [0.85, 0.55, 0.4]. Use r=0.3. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.3 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 45429.0 / 1000.
Final: {"answer": 45.429, "unit": "kg"}

Answer: 45.429

Prompt: Convert 45429 g to kg. Return the converted value with unit.

There are 1000 grams in one kilogram.
Apply the conversion factor directly to the given value.
Compute 45429.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=221 degrees and keep the unit as newtons.
Final: {"answer": [-339.9967, -295.5546], "unit": "N"}

Answer: -339.9967

Answer: -295.5546

Prompt: A vector has magnitude 450.5 N at 221 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=221 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-1.6, 21.25], "unit": "dimensionless"}

Answer: -1.6

Answer: 21.25

Prompt: A line passes through points (16, -4.35) and (16.75, -5.55). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. amount times volume is not concentration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In field worksheet case 406756, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
amount times volume is not concentration
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def weighted_sum_000574(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_000574"}

Answer: python_code

Prompt: Write a Python function weighted_sum_000574(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.

try:
    weighted_sum_000574([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: volume.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=1.92 mol and T=251 K, but does not give volume. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: volume.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 10.65 kg and a = 12.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 130.995, "unit": "N"}

Answer: 130.995

Prompt: A cart has mass 10.65 kg and measured acceleration 12.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 10.65 kg and a = 12.3 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 25.3^2 and multiply by 0.5 * 8.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2832.3983, "unit": "J"}

Answer: 2832.3983

Prompt: A body of mass 8.85 kg moves at 25.3 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 25.3^2 and multiply by 0.5 * 8.85.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=55 degrees through the sine of 2 theta.
3. Substitute v=31.3 m/s and g=9.81 m/s^2.
Final: {"answer": 93.8438, "unit": "m"}

Answer: 93.8438

Prompt: A projectile is launched on level ground with no air resistance at speed 31.3 m/s and angle 55 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=55 degrees through the sine of 2 theta.
Substitute v=31.3 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.48 * 8.314 * 597 / 46.0.
Final: {"answer": 51.7926, "unit": "kPa"}

Answer: 51.7926

Prompt: An ideal gas sample has n=0.48 mol, T=597 K, and V=46.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.48 * 8.314 * 597 / 46.0.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=24.9 V and R=32.3 ohm.
Final: {"answer": 19.1954, "unit": "W"}

Answer: 19.1954

Prompt: A resistor has resistance 32.3 ohm and voltage 24.9 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=24.9 V and R=32.3 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.67 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1381.7965, "unit": "g"}

Answer: 1381.7965

Prompt: A sample contains 7.67 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.67 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3975 mL to 3.975 L.
3. Compute M = 4.6 / 3.975.
Final: {"answer": 1.1572, "unit": "mol/L"}

Answer: 1.1572

Prompt: A solution contains 4.6 mol of solute in 3975 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3975 mL to 3.975 L.
Compute M = 4.6 / 3.975.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 1.6676, "unit": "state_units"}

Answer: 1.6676

Prompt: Use explicit Euler on dy/dt = -0.21 y with y(0)=4.5, step size h=0.45, for 10 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.3)=24.33 and f(13.7)=42.37.
3. The interval width is 4.4.
Final: {"answer": 146.74, "unit": "area_units"}

Answer: 146.74

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.1x+-13.8 from x=9.3 to x=13.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.3)=24.33 and f(13.7)=42.37.
The interval width is 4.4.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.42 and add it to the current value.
Final: {"answer": [0.387, 0.789, 1.556], "unit": "temperature_units"}

Answer: 0.387

Answer: 0.789

Answer: 1.556

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.3, right=2.15; current interior values are [1.5, 1.65, -0.25]. Use r=0.42. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.42 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1114.0 / 100.
Final: {"answer": 11.14, "unit": "m"}

Answer: 11.14

Prompt: Convert 1114 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 1114.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=14 degrees and keep the unit as newtons.
Final: {"answer": [374.5342, 93.3819], "unit": "N"}

Answer: 374.5342

Answer: 93.3819

Prompt: A vector has magnitude 386 N at 14 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=14 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [8.9, -5.75], "unit": "dimensionless"}

Answer: 8.9

Answer: -5.75

Prompt: A line passes through points (-14, -130.35) and (-6.75, -65.825). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. density times acceleration times height gives kg/(m*s^2), or pascal
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In field worksheet case 478330, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
density times acceleration times height gives kg/(m*s^2), or pascal
The equation is valid only if both sides have identical dimensions.

Answer: consistent


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def weighted_sum_000592(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_000592"}

Answer: python_code

Prompt: Write a Python function weighted_sum_000592(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.

try:
    weighted_sum_000592([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: required_fields, allowed_transformations.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid billing survey records in release 692532, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: required_fields, allowed_transformations.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 20.45 kg and a = 3.35 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 68.5075, "unit": "N"}

Answer: 68.5075

Prompt: A cart has mass 20.45 kg and measured acceleration 3.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 20.45 kg and a = 3.35 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 41^2 and multiply by 0.5 * 10.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 8993.35, "unit": "J"}

Answer: 8993.35

Prompt: A body of mass 10.7 kg moves at 41 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 41^2 and multiply by 0.5 * 10.7.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=153.5 V and R=117.8 ohm.
Final: {"answer": 200.0191, "unit": "W"}

Answer: 200.0191

Prompt: A resistor has resistance 117.8 ohm and voltage 153.5 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=153.5 V and R=117.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=573 mg, t=135 h, and T_half=20 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 5.3236, "unit": "mg"}

Answer: 5.3236

Prompt: A radioactive sample starts with 573 mg. Its half-life is 20 hours. How many mg remain after 135 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=573 mg, t=135 h, and T_half=20 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.36 y, so each step multiplies y by 1 - h*0.36.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 23.247, "unit": "state_units"}

Answer: 23.247

Prompt: Use explicit Euler on dy/dt = -0.36 y with y(0)=40.5, step size h=0.15, for 10 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.36 y, so each step multiplies y by 1 - h*0.36.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.2)=7.96 and f(10.4)=8.32.
3. The interval width is 1.2.
Final: {"answer": 9.768, "unit": "area_units"}

Answer: 9.768

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.3x+5.2 from x=9.2 to x=10.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.2)=7.96 and f(10.4)=8.32.
The interval width is 1.2.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.22 and add it to the current value.
Final: {"answer": [1.565, 1.53, -0.039], "unit": "temperature_units"}

Answer: 1.565

Answer: 1.53

Answer: -0.039

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.1, right=-0.1; current interior values are [0.85, 2.85, -1.15]. Use r=0.22. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.22 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 46123.0 / 1000.
Final: {"answer": 46.123, "unit": "kg"}

Answer: 46.123

Prompt: Convert 46123 g to kg. Return the converted value with unit.

There are 1000 grams in one kilogram.
Apply the conversion factor directly to the given value.
Compute 46123.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=342 degrees and keep the unit as newtons.
Final: {"answer": [132.6724, -43.1079], "unit": "N"}

Answer: 132.6724

Answer: -43.1079

Prompt: A vector has magnitude 139.5 N at 342 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=342 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-7.15, -17.25], "unit": "dimensionless"}

Answer: -7.15

Answer: -17.25

Prompt: A line passes through points (14.75, -122.713) and (25.75, -201.363). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. m*v is momentum, not energy
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In model card equation case 902761, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
m*v is momentum, not energy
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: volume.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=3.19 mol and T=309 K, but does not give volume. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: volume.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 0.8 kg and a = 5.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 4.52, "unit": "N"}

Answer: 4.52

Prompt: A cart has mass 0.8 kg and measured acceleration 5.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 0.8 kg and a = 5.65 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 35.3^2 and multiply by 0.5 * 1.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1152.6332, "unit": "J"}

Answer: 1152.6332

Prompt: A body of mass 1.85 kg moves at 35.3 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 35.3^2 and multiply by 0.5 * 1.85.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=79 degrees through the sine of 2 theta.
3. Substitute v=58.4 m/s and g=9.81 m/s^2.
Final: {"answer": 130.2363, "unit": "m"}

Answer: 130.2363

Prompt: A projectile is launched on level ground with no air resistance at speed 58.4 m/s and angle 79 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=79 degrees through the sine of 2 theta.
Substitute v=58.4 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.43 * 8.314 * 330 / 52.8.
Final: {"answer": 126.2689, "unit": "kPa"}

Answer: 126.2689

Prompt: An ideal gas sample has n=2.43 mol, T=330 K, and V=52.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.43 * 8.314 * 330 / 52.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 820 * 3.23 * 91.
Final: {"answer": 241022.6, "unit": "J"}

Answer: 241022.6

Prompt: A 820 g sample has specific heat 3.23 J/(g*K). How much heat is needed to raise its temperature by 91 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 820 * 3.23 * 91.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=93.2 V and R=160.6 ohm.
Final: {"answer": 54.0862, "unit": "W"}

Answer: 54.0862

Prompt: A resistor has resistance 160.6 ohm and voltage 93.2 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=93.2 V and R=160.6 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=469.5 mg, t=279 h, and T_half=24 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.1486, "unit": "mg"}

Answer: 0.1486

Prompt: A radioactive sample starts with 469.5 mg. Its half-life is 24 hours. How many mg remain after 279 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=469.5 mg, t=279 h, and T_half=24 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.38 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 114.9357, "unit": "g"}

Answer: 114.9357

Prompt: A sample contains 6.38 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.38 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4775 mL to 4.775 L.
3. Compute M = 4.15 / 4.775.
Final: {"answer": 0.8691, "unit": "mol/L"}

Answer: 0.8691

Prompt: A solution contains 4.15 mol of solute in 4775 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4775 mL to 4.775 L.
Compute M = 4.15 / 4.775.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 5.4333, "unit": "state_units"}

Answer: 5.4333

Prompt: Use explicit Euler on dy/dt = -0.58 y with y(0)=6.5, step size h=0.1, for 3 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.
Apply that update for 3 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(8.6)=18 and f(16.1)=29.25.
3. The interval width is 7.5.
Final: {"answer": 177.1875, "unit": "area_units"}

Answer: 177.1875

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.5x+5.1 from x=8.6 to x=16.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(8.6)=18 and f(16.1)=29.25.
The interval width is 7.5.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.1 and add it to the current value.
Final: {"answer": [-1.34, 0.71, -0.885], "unit": "temperature_units"}

Answer: -1.34

Answer: 0.71

Answer: -0.885

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.1, right=1.45; current interior values are [-1.85, 1.3, -1.45]. Use r=0.1. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.1 and add it to the current value.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=254 degrees and keep the unit as newtons.
Final: {"answer": [-4.8237, -16.8221], "unit": "N"}

Answer: -4.8237

Answer: -16.8221

Prompt: A vector has magnitude 17.5 N at 254 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=254 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def safe_mean_000628(values):
    if not values:
        raise ValueError('safe_mean requires at least one value')
    return sum(values) / len(values)
```
Final: {"answer": "python_code", "function": "safe_mean_000628"}

Answer: python_code

Prompt: Write a Python function safe_mean_000628(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.

try:
    safe_mean_000628([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 13.65 kg and a = 7.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 108.5175, "unit": "N"}

Answer: 108.5175

Prompt: A cart has mass 13.65 kg and measured acceleration 7.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 13.65 kg and a = 7.95 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 5.35^2 and multiply by 0.5 * 15.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 224.6866, "unit": "J"}

Answer: 224.6866

Prompt: A body of mass 15.7 kg moves at 5.35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 5.35^2 and multiply by 0.5 * 15.7.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=35 degrees through the sine of 2 theta.
3. Substitute v=67 m/s and g=9.81 m/s^2.
Final: {"answer": 429.998, "unit": "m"}

Answer: 429.998

Prompt: A projectile is launched on level ground with no air resistance at speed 67 m/s and angle 35 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=35 degrees through the sine of 2 theta.
Substitute v=67 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.9 * 8.314 * 584 / 39.5.
Final: {"answer": 110.6288, "unit": "kPa"}

Answer: 110.6288

Prompt: An ideal gas sample has n=0.9 mol, T=584 K, and V=39.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.9 * 8.314 * 584 / 39.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1850 * 3.585 * 71.
Final: {"answer": 470889.75, "unit": "J"}

Answer: 470889.75

Prompt: A 1850 g sample has specific heat 3.585 J/(g*K). How much heat is needed to raise its temperature by 71 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1850 * 3.585 * 71.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=234.9 V and R=29 ohm.
Final: {"answer": 1902.69, "unit": "W"}

Answer: 1902.69

Prompt: A resistor has resistance 29 ohm and voltage 234.9 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=234.9 V and R=29 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=913 mg, t=183 h, and T_half=16.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.4186, "unit": "mg"}

Answer: 0.4186

Prompt: A radioactive sample starts with 913 mg. Its half-life is 16.5 hours. How many mg remain after 183 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=913 mg, t=183 h, and T_half=16.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.46 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 328.3146, "unit": "g"}

Answer: 328.3146

Prompt: A sample contains 7.46 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.46 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1885 mL to 1.885 L.
3. Compute M = 2.54 / 1.885.
Final: {"answer": 1.3475, "unit": "mol/L"}

Answer: 1.3475

Prompt: A solution contains 2.54 mol of solute in 1885 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1885 mL to 1.885 L.
Compute M = 2.54 / 1.885.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.13 y, so each step multiplies y by 1 - h*0.13.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 7.7194, "unit": "state_units"}

Answer: 7.7194

Prompt: Use explicit Euler on dy/dt = -0.13 y with y(0)=31.5, step size h=1.4, for 7 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.13 y, so each step multiplies y by 1 - h*0.13.
Apply that update for 7 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.34 and add it to the current value.
Final: {"answer": [0.172, 1.044, 0.354], "unit": "temperature_units"}

Answer: 0.172

Answer: 1.044

Answer: 0.354

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.1, right=-2; current interior values are [-0.1, 0.5, 2.7]. Use r=0.34. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.34 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1296.5 / 100.
Final: {"answer": 12.965, "unit": "m"}

Answer: 12.965

Prompt: Convert 1296.5 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 1296.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=355 degrees and keep the unit as newtons.
Final: {"answer": [264.9878, -23.1834], "unit": "N"}

Answer: 264.9878

Answer: -23.1834

Prompt: A vector has magnitude 266 N at 355 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=355 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [8.75, -7.25], "unit": "dimensionless"}

Answer: 8.75

Answer: -7.25

Prompt: A line passes through points (-14.25, -131.938) and (-3.75, -40.0625). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. grams cancel with J/(g*K), and kelvin cancels, leaving joules
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In model card equation case 572039, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
grams cancel with J/(g*K), and kelvin cancels, leaving joules
The equation is valid only if both sides have identical dimensions.

Answer: consistent


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def center_values_000646(values):
    if not values:
        raise ValueError('center_values requires at least one value')
    mean = sum(values) / len(values)
    return [value - mean for value in values]
```
Final: {"answer": "python_code", "function": "center_values_000646"}

Answer: python_code

Prompt: Write a Python function center_values_000646(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.

try:
    center_values_000646([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 31.1^2 and multiply by 0.5 * 19.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 9285.216, "unit": "J"}

Answer: 9285.216

Prompt: A body of mass 19.2 kg moves at 31.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 31.1^2 and multiply by 0.5 * 19.2.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=59 degrees through the sine of 2 theta.
3. Substitute v=21.6 m/s and g=9.81 m/s^2.
Final: {"answer": 41.9927, "unit": "m"}

Answer: 41.9927

Prompt: A projectile is launched on level ground with no air resistance at speed 21.6 m/s and angle 59 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=59 degrees through the sine of 2 theta.
Substitute v=21.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.63 * 8.314 * 277 / 15.3.
Final: {"answer": 847.4357, "unit": "kPa"}

Answer: 847.4357

Prompt: An ideal gas sample has n=5.63 mol, T=277 K, and V=15.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.63 * 8.314 * 277 / 15.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1755 * 1.69 * 11.
Final: {"answer": 32625.45, "unit": "J"}

Answer: 32625.45

Prompt: A 1755 g sample has specific heat 1.69 J/(g*K). How much heat is needed to raise its temperature by 11 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1755 * 1.69 * 11.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=120.9 V and R=188.2 ohm.
Final: {"answer": 77.6664, "unit": "W"}

Answer: 77.6664

Prompt: A resistor has resistance 188.2 ohm and voltage 120.9 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=120.9 V and R=188.2 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.61 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 761.6621, "unit": "g"}

Answer: 761.6621

Prompt: A sample contains 7.61 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.61 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3490 mL to 3.49 L.
3. Compute M = 3.84 / 3.49.
Final: {"answer": 1.1003, "unit": "mol/L"}

Answer: 1.1003

Prompt: A solution contains 3.84 mol of solute in 3490 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3490 mL to 3.49 L.
Compute M = 3.84 / 3.49.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6.3)=5.91 and f(-3.9)=4.23.
3. The interval width is 2.4.
Final: {"answer": 12.168, "unit": "area_units"}

Answer: 12.168

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.7x+1.5 from x=-6.3 to x=-3.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.3)=5.91 and f(-3.9)=4.23.
The interval width is 2.4.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.42 and add it to the current value.
Final: {"answer": [0.719, 0.763, 0.767], "unit": "temperature_units"}

Answer: 0.719

Answer: 0.763

Answer: 0.767

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.8, right=0.4; current interior values are [2.0, 1.75, -0.85]. Use r=0.42. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.42 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 28676.0 / 1000.
Final: {"answer": 28.676, "unit": "kg"}

Answer: 28.676

Prompt: Convert 28676 g to kg. Return the converted value with unit.

There are 1000 grams in one kilogram.
Apply the conversion factor directly to the given value.
Compute 28676.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=92 degrees and keep the unit as newtons.
Final: {"answer": [-4.2752, 122.4254], "unit": "N"}

Answer: -4.2752

Answer: 122.4254

Prompt: A vector has magnitude 122.5 N at 92 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=92 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-3.4, -28.25], "unit": "dimensionless"}

Answer: -3.4

Answer: -28.25

Prompt: A line passes through points (-5.75, -8.7) and (5, -45.25). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def weighted_sum_000664(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_000664"}

Answer: python_code

Prompt: Write a Python function weighted_sum_000664(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.

try:
    weighted_sum_000664([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: launch_angle_or_vertical_velocity.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 77.9 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: launch_angle_or_vertical_velocity.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 14.35 kg and a = 4.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 63.8575, "unit": "N"}

Answer: 63.8575

Prompt: A cart has mass 14.35 kg and measured acceleration 4.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 14.35 kg and a = 4.45 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 19.3^2 and multiply by 0.5 * 16.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3045.1058, "unit": "J"}

Answer: 3045.1058

Prompt: A body of mass 16.35 kg moves at 19.3 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 19.3^2 and multiply by 0.5 * 16.35.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=71 degrees through the sine of 2 theta.
3. Substitute v=7.7 m/s and g=9.81 m/s^2.
Final: {"answer": 3.721, "unit": "m"}

Answer: 3.721

Prompt: A projectile is launched on level ground with no air resistance at speed 7.7 m/s and angle 71 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=71 degrees through the sine of 2 theta.
Substitute v=7.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.02 * 8.314 * 253 / 105.5.
Final: {"answer": 20.3366, "unit": "kPa"}

Answer: 20.3366

Prompt: An ideal gas sample has n=1.02 mol, T=253 K, and V=105.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.02 * 8.314 * 253 / 105.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1240 * 1.09 * 71.
Final: {"answer": 95963.6, "unit": "J"}

Answer: 95963.6

Prompt: A 1240 g sample has specific heat 1.09 J/(g*K). How much heat is needed to raise its temperature by 71 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1240 * 1.09 * 71.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=77 V and R=153 ohm.
Final: {"answer": 38.7516, "unit": "W"}

Answer: 38.7516

Prompt: A resistor has resistance 153 ohm and voltage 77 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=77 V and R=153 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=913.5 mg, t=349.5 h, and T_half=55 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 11.1635, "unit": "mg"}

Answer: 11.1635

Prompt: A radioactive sample starts with 913.5 mg. Its half-life is 55 hours. How many mg remain after 349.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=913.5 mg, t=349.5 h, and T_half=55 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.6 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 64.854, "unit": "g"}

Answer: 64.854

Prompt: A sample contains 3.6 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 3.6 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 400 mL to 0.4 L.
3. Compute M = 3.705 / 0.4.
Final: {"answer": 9.2625, "unit": "mol/L"}

Answer: 9.2625

Prompt: A solution contains 3.705 mol of solute in 400 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 400 mL to 0.4 L.
Compute M = 3.705 / 0.4.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(1.5)=-19 and f(7.4)=-29.62.
3. The interval width is 5.9.
Final: {"answer": -143.429, "unit": "area_units"}

Answer: -143.429

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.8x+-16.3 from x=1.5 to x=7.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.5)=-19 and f(7.4)=-29.62.
The interval width is 5.9.