Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 5.65 kg and a = 12.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 71.19, "unit": "N"}

Answer: 71.19

Prompt: A cart has mass 5.65 kg and measured acceleration 12.6 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 = 5.65 kg and a = 12.6 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 = 34.8^2 and multiply by 0.5 * 19.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 11535.156, "unit": "J"}

Answer: 11535.156

Prompt: A body of mass 19.05 kg moves at 34.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 34.8^2 and multiply by 0.5 * 19.05.
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=84 degrees through the sine of 2 theta.
3. Substitute v=73 m/s and g=9.81 m/s^2.
Final: {"answer": 112.942, "unit": "m"}

Answer: 112.942

Prompt: A projectile is launched on level ground with no air resistance at speed 73 m/s and angle 84 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=84 degrees through the sine of 2 theta.
Substitute v=73 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 = 3.73 * 8.314 * 267 / 113.3.
Final: {"answer": 73.0803, "unit": "kPa"}

Answer: 73.0803

Prompt: An ideal gas sample has n=3.73 mol, T=267 K, and V=113.3 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 = 3.73 * 8.314 * 267 / 113.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1530 * 3.755 * 16.
Final: {"answer": 91922.4, "unit": "J"}

Answer: 91922.4

Prompt: A 1530 g sample has specific heat 3.755 J/(g*K). How much heat is needed to raise its temperature by 16 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1530 * 3.755 * 16.


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=23.4 V and R=173.6 ohm.
Final: {"answer": 3.1541, "unit": "W"}

Answer: 3.1541

Prompt: A resistor has resistance 173.6 ohm and voltage 23.4 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=23.4 V and R=173.6 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=890.5 mg, t=66.5 h, and T_half=48.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 344.256, "unit": "mg"}

Answer: 344.256

Prompt: A radioactive sample starts with 890.5 mg. Its half-life is 48.5 hours. How many mg remain after 66.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=890.5 mg, t=66.5 h, and T_half=48.5 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 = 0.51 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 9.1876, "unit": "g"}

Answer: 9.1876

Prompt: A sample contains 0.51 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 = 0.51 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 4515 mL to 4.515 L.
3. Compute M = 2.605 / 4.515.
Final: {"answer": 0.577, "unit": "mol/L"}

Answer: 0.577

Prompt: A solution contains 2.605 mol of solute in 4515 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4515 mL to 4.515 L.
Compute M = 2.605 / 4.515.


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=0.44 and add it to the current value.
Final: {"answer": [0.072, 1.33, 2.11], "unit": "temperature_units"}

Answer: 0.072

Answer: 1.33

Answer: 2.11

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=-1.4, right=2.55; current interior values are [0.05, 1.55, 2.55]. Use r=0.44. 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=0.44 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 271.5 / 100.
Final: {"answer": 2.715, "unit": "m"}

Answer: 2.715

Prompt: Convert 271.5 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 271.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=332 degrees and keep the unit as newtons.
Final: {"answer": [247.2253, -131.452], "unit": "N"}

Answer: 247.2253

Answer: -131.452

Prompt: A vector has magnitude 280 N at 332 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=332 degrees and keep the unit as newtons.

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


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_002032(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_002032"}

Answer: python_code

Prompt: Write a Python function safe_mean_002032(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_002032([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 23.35 kg and a = 4.35 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 101.5725, "unit": "N"}

Answer: 101.5725

Prompt: A cart has mass 23.35 kg and measured acceleration 4.35 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 = 23.35 kg and a = 4.35 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 = 37.8^2 and multiply by 0.5 * 28.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 20432.412, "unit": "J"}

Answer: 20432.412

Prompt: A body of mass 28.6 kg moves at 37.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 37.8^2 and multiply by 0.5 * 28.6.
The unit kg*m^2/s^2 is one joule.


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 = 0.5 * 8.314 * 451 / 34.4.
Final: {"answer": 54.5002, "unit": "kPa"}

Answer: 54.5002

Prompt: An ideal gas sample has n=0.5 mol, T=451 K, and V=34.4 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 = 0.5 * 8.314 * 451 / 34.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1420 * 3.9 * 81.
Final: {"answer": 448578.0, "unit": "J"}

Answer: 448578.0

Prompt: A 1420 g sample has specific heat 3.9 J/(g*K). How much heat is needed to raise its temperature by 81 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1420 * 3.9 * 81.


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=204.2 V and R=28.3 ohm.
Final: {"answer": 1473.4148, "unit": "W"}

Answer: 1473.4148

Prompt: A resistor has resistance 28.3 ohm and voltage 204.2 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=204.2 V and R=28.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=154 mg, t=155.5 h, and T_half=110 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 57.8061, "unit": "mg"}

Answer: 57.8061

Prompt: A radioactive sample starts with 154 mg. Its half-life is 110 hours. How many mg remain after 155.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=154 mg, t=155.5 h, and T_half=110 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 = 7.2 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 420.768, "unit": "g"}

Answer: 420.768

Prompt: A sample contains 7.2 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 = 7.2 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 4705 mL to 4.705 L.
3. Compute M = 2.925 / 4.705.
Final: {"answer": 0.6217, "unit": "mol/L"}

Answer: 0.6217

Prompt: A solution contains 2.925 mol of solute in 4705 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4705 mL to 4.705 L.
Compute M = 2.925 / 4.705.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0649, "unit": "state_units"}

Answer: 0.0649

Prompt: Use explicit Euler on dy/dt = -0.63 y with y(0)=72, step size h=0.8, 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) = -0.63 y, so each step multiplies y by 1 - h*0.63.
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(3)=-2.9 and f(7.6)=-3.36.
3. The interval width is 4.6.
Final: {"answer": -14.398, "unit": "area_units"}

Answer: -14.398

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.1x+-2.6 from x=3 to x=7.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3)=-2.9 and f(7.6)=-3.36.
The interval width is 4.6.

(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=0.26 and add it to the current value.
Final: {"answer": [1.468, 1.716, 1.415], "unit": "temperature_units"}

Answer: 1.468

Answer: 1.716

Answer: 1.415

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=1.85, right=-0.2; current interior values are [1.0, 1.95, 2.0]. Use r=0.26. 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=0.26 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 31026.0 / 1000.
Final: {"answer": 31.026, "unit": "kg"}

Answer: 31.026

Prompt: Convert 31026 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 31026.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=287 degrees and keep the unit as newtons.
Final: {"answer": [60.8133, -198.9114], "unit": "N"}

Answer: 60.8133

Answer: -198.9114

Prompt: A vector has magnitude 208 N at 287 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=287 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": [1.55, 9.5], "unit": "dimensionless"}

Answer: 1.55

Answer: 9.5

Prompt: A line passes through points (1.75, 12.2125) and (11.25, 26.9375). 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. velocity divided by time is acceleration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In instrument manual case 799996, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
velocity divided by time is acceleration
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=5 mol and T=406 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 = 5.8 kg and a = 2.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 14.79, "unit": "N"}

Answer: 14.79

Prompt: A cart has mass 5.8 kg and measured acceleration 2.55 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 = 5.8 kg and a = 2.55 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 = 12.9^2 and multiply by 0.5 * 14.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1214.793, "unit": "J"}

Answer: 1214.793

Prompt: A body of mass 14.6 kg moves at 12.9 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 12.9^2 and multiply by 0.5 * 14.6.
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=47 degrees through the sine of 2 theta.
3. Substitute v=44.1 m/s and g=9.81 m/s^2.
Final: {"answer": 197.7648, "unit": "m"}

Answer: 197.7648

Prompt: A projectile is launched on level ground with no air resistance at speed 44.1 m/s and angle 47 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=47 degrees through the sine of 2 theta.
Substitute v=44.1 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 = 5.36 * 8.314 * 552 / 66.5.
Final: {"answer": 369.9067, "unit": "kPa"}

Answer: 369.9067

Prompt: An ideal gas sample has n=5.36 mol, T=552 K, and V=66.5 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 = 5.36 * 8.314 * 552 / 66.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1640 * 0.73 * 16.
Final: {"answer": 19155.2, "unit": "J"}

Answer: 19155.2

Prompt: A 1640 g sample has specific heat 0.73 J/(g*K). How much heat is needed to raise its temperature by 16 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1640 * 0.73 * 16.


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=100.4 V and R=128.9 ohm.
Final: {"answer": 78.2014, "unit": "W"}

Answer: 78.2014

Prompt: A resistor has resistance 128.9 ohm and voltage 100.4 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=100.4 V and R=128.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=229 mg, t=33.5 h, and T_half=110.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 185.5979, "unit": "mg"}

Answer: 185.5979

Prompt: A radioactive sample starts with 229 mg. Its half-life is 110.5 hours. How many mg remain after 33.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=229 mg, t=33.5 h, and T_half=110.5 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 = 5.46 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 546.475, "unit": "g"}

Answer: 546.475

Prompt: A sample contains 5.46 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 = 5.46 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 3820 mL to 3.82 L.
3. Compute M = 0.75 / 3.82.
Final: {"answer": 0.1963, "unit": "mol/L"}

Answer: 0.1963

Prompt: A solution contains 0.75 mol of solute in 3820 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3820 mL to 3.82 L.
Compute M = 0.75 / 3.82.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.65 y, so each step multiplies y by 1 - h*0.65.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.65 y with y(0)=5.5, step size h=1.1, 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) = -0.65 y, so each step multiplies y by 1 - h*0.65.
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(2.8)=2.3 and f(5.3)=19.8.
3. The interval width is 2.5.
Final: {"answer": 27.625, "unit": "area_units"}

Answer: 27.625

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7x+-17.3 from x=2.8 to x=5.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(2.8)=2.3 and f(5.3)=19.8.
The interval width is 2.5.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1942.5 / 100.
Final: {"answer": 19.425, "unit": "m"}

Answer: 19.425

Prompt: Convert 1942.5 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 1942.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=92 degrees and keep the unit as newtons.
Final: {"answer": [-16.839, 482.2061], "unit": "N"}

Answer: -16.839

Answer: 482.2061

Prompt: A vector has magnitude 482.5 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": [-5.35, 17.0], "unit": "dimensionless"}

Answer: -5.35

Answer: 17.0

Prompt: A line passes through points (3.75, -3.0625) and (13.75, -56.5625). 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 quality-control check case 331784, 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 threshold_flags_002068(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_002068"}

Answer: python_code

Prompt: Write a Python function threshold_flags_002068(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. 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 threshold_flags_002068([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_002068([], 5) == []

assert threshold_flags_002068([-1, 0], 0) == [False, True]


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

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a knapsack scoring problem with 2709 items and budget 65385, but the recurrence, objective, and tie-breaking rule are all absent. 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: recurrence, objective, tie_breaking_rule.
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 = 16.85 kg and a = 12.15 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 204.7275, "unit": "N"}

Answer: 204.7275

Prompt: A cart has mass 16.85 kg and measured acceleration 12.15 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 = 16.85 kg and a = 12.15 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 = 42.25^2 and multiply by 0.5 * 15.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 14146.6203, "unit": "J"}

Answer: 14146.6203

Prompt: A body of mass 15.85 kg moves at 42.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 42.25^2 and multiply by 0.5 * 15.85.
The unit kg*m^2/s^2 is one joule.


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 = 3.89 * 8.314 * 293 / 13.0.
Final: {"answer": 728.9268, "unit": "kPa"}

Answer: 728.9268

Prompt: An ideal gas sample has n=3.89 mol, T=293 K, and V=13.0 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 = 3.89 * 8.314 * 293 / 13.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 525 * 3.745 * 101.
Final: {"answer": 198578.625, "unit": "J"}

Answer: 198578.625

Prompt: A 525 g sample has specific heat 3.745 J/(g*K). How much heat is needed to raise its temperature by 101 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 525 * 3.745 * 101.


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=236.7 V and R=147.8 ohm.
Final: {"answer": 379.0723, "unit": "W"}

Answer: 379.0723

Prompt: A resistor has resistance 147.8 ohm and voltage 236.7 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=236.7 V and R=147.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=398 mg, t=78 h, and T_half=68 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 179.7148, "unit": "mg"}

Answer: 179.7148

Prompt: A radioactive sample starts with 398 mg. Its half-life is 68 hours. How many mg remain after 78 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=398 mg, t=78 h, and T_half=68 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 3330 mL to 3.33 L.
3. Compute M = 4.315 / 3.33.
Final: {"answer": 1.2958, "unit": "mol/L"}

Answer: 1.2958

Prompt: A solution contains 4.315 mol of solute in 3330 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3330 mL to 3.33 L.
Compute M = 4.315 / 3.33.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.4 y, so each step multiplies y by 1 - h*0.4.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 24.0201, "unit": "state_units"}

Answer: 24.0201

Prompt: Use explicit Euler on dy/dt = -0.4 y with y(0)=62, step size h=0.25, for 9 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.4 y, so each step multiplies y by 1 - h*0.4.
Apply that update for 9 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(7.3)=-48.61 and f(16.1)=-89.97.
3. The interval width is 8.8.
Final: {"answer": -609.752, "unit": "area_units"}

Answer: -609.752

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.7x+-14.3 from x=7.3 to x=16.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7.3)=-48.61 and f(16.1)=-89.97.
The interval width is 8.8.


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=0.4 and add it to the current value.
Final: {"answer": [1.98, -0.07, 0.12], "unit": "temperature_units"}

Answer: 1.98

Answer: -0.07

Answer: 0.12

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=2.15, right=-1.8; current interior values are [-0.1, 2.85, -1.5]. Use r=0.4. 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=0.4 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 93.0 + 273.15.
Final: {"answer": 366.15, "unit": "K"}

Answer: 366.15

Prompt: Convert 93 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 93.0 + 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=153 degrees and keep the unit as newtons.
Final: {"answer": [-168.8457, 86.0312], "unit": "N"}

Answer: -168.8457

Answer: 86.0312

Prompt: A vector has magnitude 189.5 N at 153 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=153 degrees and keep the unit as newtons.


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 sensor calibration case 731225, 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: 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 registry crop record from batch 384272 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 = 12.45 kg and a = 14.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 181.77, "unit": "N"}

Answer: 181.77

Prompt: A cart has mass 12.45 kg and measured acceleration 14.6 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 = 12.45 kg and a = 14.6 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=21 degrees through the sine of 2 theta.
3. Substitute v=71.1 m/s and g=9.81 m/s^2.
Final: {"answer": 344.811, "unit": "m"}

Answer: 344.811

Prompt: A projectile is launched on level ground with no air resistance at speed 71.1 m/s and angle 21 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=21 degrees through the sine of 2 theta.
Substitute v=71.1 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 = 3.04 * 8.314 * 327 / 104.8.
Final: {"answer": 78.8624, "unit": "kPa"}

Answer: 78.8624

Prompt: An ideal gas sample has n=3.04 mol, T=327 K, and V=104.8 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 = 3.04 * 8.314 * 327 / 104.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1905 * 4.535 * 106.
Final: {"answer": 915752.55, "unit": "J"}

Answer: 915752.55

Prompt: A 1905 g sample has specific heat 4.535 J/(g*K). How much heat is needed to raise its temperature by 106 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1905 * 4.535 * 106.


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=160.1 V and R=88.1 ohm.
Final: {"answer": 290.9422, "unit": "W"}

Answer: 290.9422

Prompt: A resistor has resistance 88.1 ohm and voltage 160.1 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=160.1 V and R=88.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=74 mg, t=289.5 h, and T_half=96.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 9.25, "unit": "mg"}

Answer: 9.25

Prompt: A radioactive sample starts with 74 mg. Its half-life is 96.5 hours. How many mg remain after 289.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=74 mg, t=289.5 h, and T_half=96.5 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 2890 mL to 2.89 L.
3. Compute M = 0.705 / 2.89.
Final: {"answer": 0.2439, "unit": "mol/L"}

Answer: 0.2439

Prompt: A solution contains 0.705 mol of solute in 2890 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2890 mL to 2.89 L.
Compute M = 0.705 / 2.89.


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 11 steps and round the final state.
Final: {"answer": 0.3011, "unit": "state_units"}

Answer: 0.3011

Prompt: Use explicit Euler on dy/dt = -0.85 y with y(0)=60.5, step size h=0.45, 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) = -0.85 y, so each step multiplies y by 1 - h*0.85.
Apply that update for 11 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=0.2 and add it to the current value.
Final: {"answer": [0.62, 1.19, 2.22], "unit": "temperature_units"}

Answer: 0.62

Answer: 1.19

Answer: 2.22

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=-0.15, right=2.45; current interior values are [0.8, 0.85, 2.6]. Use r=0.2. 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=0.2 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=125 degrees and keep the unit as newtons.
Final: {"answer": [-168.9183, 241.2403], "unit": "N"}

Answer: -168.9183

Answer: 241.2403

Prompt: A vector has magnitude 294.5 N at 125 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=125 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": [6.45, 11.0], "unit": "dimensionless"}

Answer: 6.45

Answer: 11.0

Prompt: A line passes through points (-4.75, -19.6375) and (3.25, 31.9625). 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. 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 field worksheet case 612540, 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. 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_002104(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_002104"}

Answer: python_code

Prompt: Write a Python function safe_mean_002104(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_002104([])
    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 25.4 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 = 4.25 kg and a = 12.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 52.9125, "unit": "N"}

Answer: 52.9125

Prompt: A cart has mass 4.25 kg and measured acceleration 12.45 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 = 4.25 kg and a = 12.45 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 = 10.1^2 and multiply by 0.5 * 23.45.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1196.0672, "unit": "J"}

Answer: 1196.0672

Prompt: A body of mass 23.45 kg moves at 10.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 10.1^2 and multiply by 0.5 * 23.45.
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=54 degrees through the sine of 2 theta.
3. Substitute v=46.2 m/s and g=9.81 m/s^2.
Final: {"answer": 206.929, "unit": "m"}

Answer: 206.929

Prompt: A projectile is launched on level ground with no air resistance at speed 46.2 m/s and angle 54 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=54 degrees through the sine of 2 theta.
Substitute v=46.2 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 = 5.47 * 8.314 * 334 / 74.9.
Final: {"answer": 202.7972, "unit": "kPa"}

Answer: 202.7972

Prompt: An ideal gas sample has n=5.47 mol, T=334 K, and V=74.9 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 = 5.47 * 8.314 * 334 / 74.9.


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=22.9 V and R=184.5 ohm.
Final: {"answer": 2.8423, "unit": "W"}

Answer: 2.8423

Prompt: A resistor has resistance 184.5 ohm and voltage 22.9 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=22.9 V and R=184.5 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.57 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 113.1057, "unit": "g"}

Answer: 113.1057

Prompt: A sample contains 2.57 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 = 2.57 mol * 44.01 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) = -0.79 y, so each step multiplies y by 1 - h*0.79.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 0.0804, "unit": "state_units"}

Answer: 0.0804

Prompt: Use explicit Euler on dy/dt = -0.79 y with y(0)=42.5, step size h=0.55, 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) = -0.79 y, so each step multiplies y by 1 - h*0.79.
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(3)=-9.9 and f(8.3)=-3.01.
3. The interval width is 5.3.
Final: {"answer": -34.2115, "unit": "area_units"}

Answer: -34.2115

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.3x+-13.8 from x=3 to x=8.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3)=-9.9 and f(8.3)=-3.01.
The interval width is 5.3.


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": [-0.549, -0.269, -0.408], "unit": "temperature_units"}

Answer: -0.549

Answer: -0.269

Answer: -0.408

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=-1.95; current interior values are [-1.4, 0.95, 0.65]. 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 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 27446.0 / 1000.
Final: {"answer": 27.446, "unit": "kg"}

Answer: 27.446

Prompt: Convert 27446 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 27446.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=7 degrees and keep the unit as newtons.
Final: {"answer": [94.7882, 11.6385], "unit": "N"}

Answer: 94.7882

Answer: 11.6385

Prompt: A vector has magnitude 95.5 N at 7 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=7 degrees and keep the unit as newtons.


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 student derivation case 983745, 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 finite_differences_002122(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_002122"}

Answer: python_code

Prompt: Write a Python function finite_differences_002122(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_002122([5]) == []

assert finite_differences_002122([]) == []


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 registry crop record from batch 138513 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 = 21.35 kg and a = 9.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 210.2975, "unit": "N"}

Answer: 210.2975

Prompt: A cart has mass 21.35 kg and measured acceleration 9.85 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 = 21.35 kg and a = 9.85 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 = 28.45^2 and multiply by 0.5 * 25.55.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 10340.1169, "unit": "J"}

Answer: 10340.1169

Prompt: A body of mass 25.55 kg moves at 28.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 28.45^2 and multiply by 0.5 * 25.55.
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=58 degrees through the sine of 2 theta.
3. Substitute v=44.9 m/s and g=9.81 m/s^2.
Final: {"answer": 184.7072, "unit": "m"}

Answer: 184.7072

Prompt: A projectile is launched on level ground with no air resistance at speed 44.9 m/s and angle 58 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=58 degrees through the sine of 2 theta.
Substitute v=44.9 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 = 4.72 * 8.314 * 513 / 109.7.
Final: {"answer": 183.5113, "unit": "kPa"}

Answer: 183.5113

Prompt: An ideal gas sample has n=4.72 mol, T=513 K, and V=109.7 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 = 4.72 * 8.314 * 513 / 109.7.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1585 * 4.21 * 30.
Final: {"answer": 200185.5, "unit": "J"}

Answer: 200185.5

Prompt: A 1585 g sample has specific heat 4.21 J/(g*K). How much heat is needed to raise its temperature by 30 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1585 * 4.21 * 30.


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=28.9 V and R=27.5 ohm.
Final: {"answer": 30.3713, "unit": "W"}

Answer: 30.3713

Prompt: A resistor has resistance 27.5 ohm and voltage 28.9 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=28.9 V and R=27.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=246.5 mg, t=260.5 h, and T_half=19.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0235, "unit": "mg"}

Answer: 0.0235

Prompt: A radioactive sample starts with 246.5 mg. Its half-life is 19.5 hours. How many mg remain after 260.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=246.5 mg, t=260.5 h, and T_half=19.5 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 = 5.53 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 243.3753, "unit": "g"}

Answer: 243.3753

Prompt: A sample contains 5.53 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 = 5.53 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 1745 mL to 1.745 L.
3. Compute M = 2.44 / 1.745.
Final: {"answer": 1.3983, "unit": "mol/L"}

Answer: 1.3983

Prompt: A solution contains 2.44 mol of solute in 1745 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1745 mL to 1.745 L.
Compute M = 2.44 / 1.745.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.45 y, so each step multiplies y by 1 - h*0.45.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 5.6116, "unit": "state_units"}

Answer: 5.6116

Prompt: Use explicit Euler on dy/dt = -0.45 y with y(0)=23.5, step size h=0.25, 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) = -0.45 y, so each step multiplies y by 1 - h*0.45.
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(5.2)=-39.84 and f(8.8)=-54.96.
3. The interval width is 3.6.
Final: {"answer": -170.64, "unit": "area_units"}

Answer: -170.64

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.2x+-18 from x=5.2 to x=8.8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(5.2)=-39.84 and f(8.8)=-54.96.
The interval width is 3.6.


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=0.12 and add it to the current value.
Final: {"answer": [-1.034, 1.516, 1.832], "unit": "temperature_units"}

Answer: -1.034

Answer: 1.516

Answer: 1.832

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=0.25, right=-1.2; current interior values are [-1.7, 1.9, 2.3]. Use r=0.12. 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=0.12 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 31.0 + 273.15.
Final: {"answer": 304.15, "unit": "K"}

Answer: 304.15

Prompt: Convert 31 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 31.0 + 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=317 degrees and keep the unit as newtons.
Final: {"answer": [37.299, -34.7819], "unit": "N"}

Answer: 37.299

Answer: -34.7819

Prompt: A vector has magnitude 51 N at 317 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=317 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": [-9.2, 6.75], "unit": "dimensionless"}

Answer: -9.2

Answer: 6.75

Prompt: A line passes through points (-8.25, 82.65) and (4.75, -36.95). 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 lab notebook case 371796, 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 finite_differences_002140(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_002140"}

Answer: python_code

Prompt: Write a Python function finite_differences_002140(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_002140([5]) == []

assert finite_differences_002140([]) == []


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 18.65 kg and a = 8.05 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 150.1325, "unit": "N"}

Answer: 150.1325

Prompt: A cart has mass 18.65 kg and measured acceleration 8.05 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 = 18.65 kg and a = 8.05 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 = 34.2^2 and multiply by 0.5 * 1.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1081.917, "unit": "J"}

Answer: 1081.917

Prompt: A body of mass 1.85 kg moves at 34.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 34.2^2 and multiply by 0.5 * 1.85.
The unit kg*m^2/s^2 is one joule.


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 = 2.54 * 8.314 * 331 / 98.0.
Final: {"answer": 71.3256, "unit": "kPa"}

Answer: 71.3256

Prompt: An ideal gas sample has n=2.54 mol, T=331 K, and V=98.0 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 = 2.54 * 8.314 * 331 / 98.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 60 * 1.35 * 18.
Final: {"answer": 1458.0, "unit": "J"}

Answer: 1458.0

Prompt: A 60 g sample has specific heat 1.35 J/(g*K). How much heat is needed to raise its temperature by 18 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 60 * 1.35 * 18.


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=50.7 V and R=18.9 ohm.
Final: {"answer": 136.0048, "unit": "W"}

Answer: 136.0048

Prompt: A resistor has resistance 18.9 ohm and voltage 50.7 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=50.7 V and R=18.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=582.5 mg, t=97 h, and T_half=100.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 298.3662, "unit": "mg"}

Answer: 298.3662

Prompt: A radioactive sample starts with 582.5 mg. Its half-life is 100.5 hours. How many mg remain after 97 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=582.5 mg, t=97 h, and T_half=100.5 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 = 5.98 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 349.4712, "unit": "g"}

Answer: 349.4712

Prompt: A sample contains 5.98 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 = 5.98 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 1545 mL to 1.545 L.
3. Compute M = 0.335 / 1.545.
Final: {"answer": 0.2168, "unit": "mol/L"}

Answer: 0.2168

Prompt: A solution contains 0.335 mol of solute in 1545 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1545 mL to 1.545 L.
Compute M = 0.335 / 1.545.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-3.6)=-12.38 and f(1.5)=-18.5.
3. The interval width is 5.1.
Final: {"answer": -78.744, "unit": "area_units"}

Answer: -78.744

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.2x+-16.7 from x=-3.6 to x=1.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-3.6)=-12.38 and f(1.5)=-18.5.
The interval width is 5.1.


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=0.44 and add it to the current value.
Final: {"answer": [2.384, 1.838, 0.748], "unit": "temperature_units"}

Answer: 2.384

Answer: 1.838

Answer: 0.748

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=2.45, right=-0.9; current interior values are [2.45, 2.3, 1.1]. Use r=0.44. 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=0.44 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 36519.0 / 1000.
Final: {"answer": 36.519, "unit": "kg"}

Answer: 36.519

Prompt: Convert 36519 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 36519.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=96 degrees and keep the unit as newtons.
Final: {"answer": [-46.3584, 441.0705], "unit": "N"}

Answer: -46.3584

Answer: 441.0705

Prompt: A vector has magnitude 443.5 N at 96 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=96 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": [1.55, 15.5], "unit": "dimensionless"}

Answer: 1.55

Answer: 15.5

Prompt: A line passes through points (-8.5, 2.325) and (-2.5, 11.625). 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 field worksheet case 617619, 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: 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 34.9 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 = 18.3 kg and a = 9.4 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 172.02, "unit": "N"}

Answer: 172.02

Prompt: A cart has mass 18.3 kg and measured acceleration 9.4 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 = 18.3 kg and a = 9.4 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 = 29.3^2 and multiply by 0.5 * 18.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 8091.2683, "unit": "J"}

Answer: 8091.2683

Prompt: A body of mass 18.85 kg moves at 29.3 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 29.3^2 and multiply by 0.5 * 18.85.
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=62 degrees through the sine of 2 theta.
3. Substitute v=45.7 m/s and g=9.81 m/s^2.
Final: {"answer": 176.4971, "unit": "m"}

Answer: 176.4971

Prompt: A projectile is launched on level ground with no air resistance at speed 45.7 m/s and angle 62 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=62 degrees through the sine of 2 theta.
Substitute v=45.7 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 = 5.3 * 8.314 * 280 / 87.1.
Final: {"answer": 141.653, "unit": "kPa"}

Answer: 141.653

Prompt: An ideal gas sample has n=5.3 mol, T=280 K, and V=87.1 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 = 5.3 * 8.314 * 280 / 87.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 345 * 2.89 * 11.
Final: {"answer": 10967.55, "unit": "J"}

Answer: 10967.55

Prompt: A 345 g sample has specific heat 2.89 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 = 345 * 2.89 * 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=88.6 V and R=2.8 ohm.
Final: {"answer": 2803.5571, "unit": "W"}

Answer: 2803.5571

Prompt: A resistor has resistance 2.8 ohm and voltage 88.6 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=88.6 V and R=2.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=5 mg, t=213.5 h, and T_half=30 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.036, "unit": "mg"}

Answer: 0.036

Prompt: A radioactive sample starts with 5 mg. Its half-life is 30 hours. How many mg remain after 213.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=5 mg, t=213.5 h, and T_half=30 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 = 4.86 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 213.8886, "unit": "g"}

Answer: 213.8886

Prompt: A sample contains 4.86 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 = 4.86 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 3900 mL to 3.9 L.
3. Compute M = 4.45 / 3.9.
Final: {"answer": 1.141, "unit": "mol/L"}

Answer: 1.141

Prompt: A solution contains 4.45 mol of solute in 3900 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3900 mL to 3.9 L.
Compute M = 4.45 / 3.9.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.5 y, so each step multiplies y by 1 - h*0.5.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 0.0003, "unit": "state_units"}

Answer: 0.0003

Prompt: Use explicit Euler on dy/dt = -0.5 y with y(0)=42.5, 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) = -0.5 y, so each step multiplies y by 1 - h*0.5.
Apply that update for 8 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=0.1 and add it to the current value.
Final: {"answer": [-0.685, 1.96, 0.57], "unit": "temperature_units"}

Answer: -0.685

Answer: 1.96

Answer: 0.57

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=-0.95, right=-2; current interior values are [-1.05, 2.5, 0.65]. 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. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 21022.0 / 1000.
Final: {"answer": 21.022, "unit": "kg"}

Answer: 21.022

Prompt: Convert 21022 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 21022.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=47 degrees and keep the unit as newtons.
Final: {"answer": [7.843, 8.4106], "unit": "N"}

Answer: 7.843

Answer: 8.4106

Prompt: A vector has magnitude 11.5 N at 47 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=47 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": [6.2, -13.75], "unit": "dimensionless"}

Answer: 6.2

Answer: -13.75

Prompt: A line passes through points (2.5, 1.75) and (13.5, 69.95). 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 lab notebook case 385001, 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
import math

def unit_vector_002176(x, y):
    norm = math.hypot(x, y)
    if norm == 0:
        raise ValueError('zero vector has no direction')
    return (x / norm, y / norm)
```
Final: {"answer": "python_code", "function": "unit_vector_002176"}

Answer: python_code

Prompt: Write a Python function unit_vector_002176(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. 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:
    unit_vector_002176(0, 0)
    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=4.04 mol and T=291 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 = 6.05 kg and a = 10.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 64.13, "unit": "N"}

Answer: 64.13

Prompt: A cart has mass 6.05 kg and measured acceleration 10.6 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 = 6.05 kg and a = 10.6 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=32 degrees through the sine of 2 theta.
3. Substitute v=49.1 m/s and g=9.81 m/s^2.
Final: {"answer": 220.8789, "unit": "m"}

Answer: 220.8789

Prompt: A projectile is launched on level ground with no air resistance at speed 49.1 m/s and angle 32 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=32 degrees through the sine of 2 theta.
Substitute v=49.1 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 = 3.88 * 8.314 * 517 / 69.4.
Final: {"answer": 240.3105, "unit": "kPa"}

Answer: 240.3105

Prompt: An ideal gas sample has n=3.88 mol, T=517 K, and V=69.4 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 = 3.88 * 8.314 * 517 / 69.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1010 * 4.315 * 105.
Final: {"answer": 457605.75, "unit": "J"}

Answer: 457605.75

Prompt: A 1010 g sample has specific heat 4.315 J/(g*K). How much heat is needed to raise its temperature by 105 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1010 * 4.315 * 105.


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=164 V and R=127.7 ohm.
Final: {"answer": 210.6186, "unit": "W"}

Answer: 210.6186

Prompt: A resistor has resistance 127.7 ohm and voltage 164 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=164 V and R=127.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=986.5 mg, t=174.5 h, and T_half=34.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 29.6139, "unit": "mg"}

Answer: 29.6139

Prompt: A radioactive sample starts with 986.5 mg. Its half-life is 34.5 hours. How many mg remain after 174.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=986.5 mg, t=174.5 h, and T_half=34.5 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) = -0.34 y, so each step multiplies y by 1 - h*0.34.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 8.8373, "unit": "state_units"}

Answer: 8.8373

Prompt: Use explicit Euler on dy/dt = -0.34 y with y(0)=39.5, step size h=1.55, for 2 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.34 y, so each step multiplies y by 1 - h*0.34.
Apply that update for 2 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(-2.3)=-22.41 and f(7)=49.2.
3. The interval width is 9.3.
Final: {"answer": 124.5735, "unit": "area_units"}

Answer: 124.5735

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.7x+-4.7 from x=-2.3 to x=7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-2.3)=-22.41 and f(7)=49.2.
The interval width is 9.3.


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=0.24 and add it to the current value.
Final: {"answer": [1.428, -0.294, -0.136], "unit": "temperature_units"}

Answer: 1.428

Answer: -0.294

Answer: -0.136

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=1.45, right=2.95; current interior values are [2.7, -1.35, -1.0]. Use r=0.24. 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=0.24 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 50.0 + 273.15.
Final: {"answer": 323.15, "unit": "K"}

Answer: 323.15

Prompt: Convert 50 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 50.0 + 273.15.


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": [0.6, -3.0], "unit": "dimensionless"}

Answer: 0.6

Answer: -3.0

Prompt: A line passes through points (17, 7.2) and (19.5, 8.7). 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 center_values_002194(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_002194"}

Answer: python_code

Prompt: Write a Python function center_values_002194(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_002194([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 23.7 kg and a = 7.2 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 170.64, "unit": "N"}

Answer: 170.64

Prompt: A cart has mass 23.7 kg and measured acceleration 7.2 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 = 23.7 kg and a = 7.2 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=16 degrees through the sine of 2 theta.
3. Substitute v=62 m/s and g=9.81 m/s^2.
Final: {"answer": 207.6462, "unit": "m"}

Answer: 207.6462

Prompt: A projectile is launched on level ground with no air resistance at speed 62 m/s and angle 16 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=16 degrees through the sine of 2 theta.
Substitute v=62 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 = 3.65 * 8.314 * 414 / 93.0.
Final: {"answer": 135.0891, "unit": "kPa"}

Answer: 135.0891

Prompt: An ideal gas sample has n=3.65 mol, T=414 K, and V=93.0 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 = 3.65 * 8.314 * 414 / 93.0.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=781 mg, t=38.5 h, and T_half=18.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 184.5794, "unit": "mg"}

Answer: 184.5794

Prompt: A radioactive sample starts with 781 mg. Its half-life is 18.5 hours. How many mg remain after 38.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=781 mg, t=38.5 h, and T_half=18.5 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 = 0.5 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 9.0075, "unit": "g"}

Answer: 9.0075

Prompt: A sample contains 0.5 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 = 0.5 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 4530 mL to 4.53 L.
3. Compute M = 4.08 / 4.53.
Final: {"answer": 0.9007, "unit": "mol/L"}

Answer: 0.9007

Prompt: A solution contains 4.08 mol of solute in 4530 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4530 mL to 4.53 L.
Compute M = 4.08 / 4.53.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.67 y, so each step multiplies y by 1 - h*0.67.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 0.8401, "unit": "state_units"}

Answer: 0.8401

Prompt: Use explicit Euler on dy/dt = -0.67 y with y(0)=69.5, step size h=1.15, 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) = -0.67 y, so each step multiplies y by 1 - h*0.67.
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(-1.7)=16.74 and f(-0.2)=7.44.
3. The interval width is 1.5.
Final: {"answer": 18.135, "unit": "area_units"}

Answer: 18.135

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.2x+6.2 from x=-1.7 to x=-0.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-1.7)=16.74 and f(-0.2)=7.44.
The interval width is 1.5.


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=0.48 and add it to the current value.
Final: {"answer": [1.554, 1.146, 0.622], "unit": "temperature_units"}

Answer: 1.554

Answer: 1.146

Answer: 0.622

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=0.9, right=-1.05; current interior values are [1.05, 2.25, 1.15]. Use r=0.48. 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=0.48 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 739.5 / 100.
Final: {"answer": 7.395, "unit": "m"}

Answer: 7.395

Prompt: Convert 739.5 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 739.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=177 degrees and keep the unit as newtons.
Final: {"answer": [-135.8136, 7.1177], "unit": "N"}

Answer: -135.8136

Answer: 7.1177

Prompt: A vector has magnitude 136 N at 177 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=177 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": [8.45, 7.5], "unit": "dimensionless"}

Answer: 8.45

Answer: 7.5

Prompt: A line passes through points (-15, -119.25) and (-8.25, -62.2125). 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. velocity divided by time is acceleration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In sensor calibration case 104182, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
velocity divided by time is acceleration
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 clamp_002212(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_002212"}

Answer: python_code

Prompt: Write a Python function clamp_002212(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. 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:
    clamp_002212(1, 3, 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 laboratory ledger records in release 470930, 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. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 37.6^2 and multiply by 0.5 * 0.45.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 318.096, "unit": "J"}

Answer: 318.096

Prompt: A body of mass 0.45 kg moves at 37.6 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 37.6^2 and multiply by 0.5 * 0.45.
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=40 degrees through the sine of 2 theta.
3. Substitute v=77.2 m/s and g=9.81 m/s^2.
Final: {"answer": 598.2973, "unit": "m"}

Answer: 598.2973

Prompt: A projectile is launched on level ground with no air resistance at speed 77.2 m/s and angle 40 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=40 degrees through the sine of 2 theta.
Substitute v=77.2 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 = 3.09 * 8.314 * 478 / 83.7.
Final: {"answer": 146.7138, "unit": "kPa"}

Answer: 146.7138

Prompt: An ideal gas sample has n=3.09 mol, T=478 K, and V=83.7 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 = 3.09 * 8.314 * 478 / 83.7.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1585 * 0.815 * 105.
Final: {"answer": 135636.375, "unit": "J"}

Answer: 135636.375

Prompt: A 1585 g sample has specific heat 0.815 J/(g*K). How much heat is needed to raise its temperature by 105 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1585 * 0.815 * 105.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=901 mg, t=40.5 h, and T_half=58 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 555.2938, "unit": "mg"}

Answer: 555.2938

Prompt: A radioactive sample starts with 901 mg. Its half-life is 58 hours. How many mg remain after 40.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=901 mg, t=40.5 h, and T_half=58 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 = 3.18 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 57.2877, "unit": "g"}

Answer: 57.2877

Prompt: A sample contains 3.18 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 = 3.18 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 705 mL to 0.705 L.
3. Compute M = 4.26 / 0.705.
Final: {"answer": 6.0426, "unit": "mol/L"}

Answer: 6.0426

Prompt: A solution contains 4.26 mol of solute in 705 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 705 mL to 0.705 L.
Compute M = 4.26 / 0.705.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.95 y, so each step multiplies y by 1 - h*0.95.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": -7.466, "unit": "state_units"}

Answer: -7.466

Prompt: Use explicit Euler on dy/dt = -0.95 y with y(0)=58.5, step size h=1.75, 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) = -0.95 y, so each step multiplies y by 1 - h*0.95.
Apply that update for 5 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=0.06 and add it to the current value.
Final: {"answer": [1.919, 2.338, -1.405], "unit": "temperature_units"}

Answer: 1.919

Answer: 2.338

Answer: -1.405

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, right=1.8; current interior values are [2.0, 2.65, -1.9]. Use r=0.06. 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=0.06 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 448.5 / 100.
Final: {"answer": 4.485, "unit": "m"}

Answer: 4.485

Prompt: Convert 448.5 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 448.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=189 degrees and keep the unit as newtons.
Final: {"answer": [-44.9398, -7.1178], "unit": "N"}

Answer: -44.9398

Answer: -7.1178

Prompt: A vector has magnitude 45.5 N at 189 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=189 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": [8.1, 28.0], "unit": "dimensionless"}

Answer: 8.1

Answer: 28.0

Prompt: A line passes through points (-20, -134) and (-6, -20.6). 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 normalize_002230(values):
    total = sum(values)
    if total == 0:
        raise ValueError('cannot normalize zero-sum values')
    return [v / total for v in values]
```
Final: {"answer": "python_code", "function": "normalize_002230"}

Answer: python_code

Prompt: Write a Python function normalize_002230(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. 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.

out = normalize_002230([2, 3, 5]); assert len(out) == 3

try:
    normalize_002230([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 24.85 kg and a = 8.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 209.9825, "unit": "N"}

Answer: 209.9825

Prompt: A cart has mass 24.85 kg and measured acceleration 8.45 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 = 24.85 kg and a = 8.45 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 = 1.45^2 and multiply by 0.5 * 28.65.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 30.1183, "unit": "J"}

Answer: 30.1183

Prompt: A body of mass 28.65 kg moves at 1.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 1.45^2 and multiply by 0.5 * 28.65.
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=20 degrees through the sine of 2 theta.
3. Substitute v=48.4 m/s and g=9.81 m/s^2.
Final: {"answer": 153.4932, "unit": "m"}

Answer: 153.4932

Prompt: A projectile is launched on level ground with no air resistance at speed 48.4 m/s and angle 20 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=20 degrees through the sine of 2 theta.
Substitute v=48.4 m/s and g=9.81 m/s^2.