Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1950 * 3.885 * 104.
Final: {"answer": 787878.0, "unit": "J"}

Answer: 787878.0

Prompt: A 1950 g sample has specific heat 3.885 J/(g*K). How much heat is needed to raise its temperature by 104 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1950 * 3.885 * 104.


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=203.9 V and R=181.3 ohm.
Final: {"answer": 229.3172, "unit": "W"}

Answer: 229.3172

Prompt: A resistor has resistance 181.3 ohm and voltage 203.9 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=203.9 V and R=181.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=767.5 mg, t=94.5 h, and T_half=115.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 435.2924, "unit": "mg"}

Answer: 435.2924

Prompt: A radioactive sample starts with 767.5 mg. Its half-life is 115.5 hours. How many mg remain after 94.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=767.5 mg, t=94.5 h, and T_half=115.5 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 = 7.17 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1291.7185, "unit": "g"}

Answer: 1291.7185

Prompt: A sample contains 7.17 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.17 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 255 mL to 0.255 L.
3. Compute M = 1 / 0.255.
Final: {"answer": 3.9216, "unit": "mol/L"}

Answer: 3.9216

Prompt: A solution contains 1 mol of solute in 255 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 255 mL to 0.255 L.
Compute M = 1 / 0.255.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.56 y, so each step multiplies y by 1 - h*0.56.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 26.9866, "unit": "state_units"}

Answer: 26.9866

Prompt: Use explicit Euler on dy/dt = -0.56 y with y(0)=32, step size h=0.05, for 6 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.56 y, so each step multiplies y by 1 - h*0.56.
Apply that update for 6 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(4.9)=-0.05 and f(12.4)=26.2.
3. The interval width is 7.5.
Final: {"answer": 98.0625, "unit": "area_units"}

Answer: 98.0625

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.5x+-17.2 from x=4.9 to x=12.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.9)=-0.05 and f(12.4)=26.2.
The interval width is 7.5.

(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=0.4 and add it to the current value.
Final: {"answer": [-0.09, 0.02, -0.78], "unit": "temperature_units"}

Answer: -0.09

Answer: 0.02

Answer: -0.78

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=-0.2, right=-1.3; current interior values are [0.75, -0.4, -0.5]. 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. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=15 degrees and keep the unit as newtons.
Final: {"answer": [8.2104, 2.2], "unit": "N"}

Answer: 8.2104

Answer: 2.2

Prompt: A vector has magnitude 8.5 N at 15 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=15 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 slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [8.6, -16.5], "unit": "dimensionless"}

Answer: 8.6

Answer: -16.5

Prompt: A line passes through points (16.25, 123.25) and (22.25, 174.85). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In field worksheet case 542750, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 17.95 kg and a = 2.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 52.9525, "unit": "N"}

Answer: 52.9525

Prompt: A cart has mass 17.95 kg and measured acceleration 2.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 17.95 kg and a = 2.95 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 13.2^2 and multiply by 0.5 * 2.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 200.376, "unit": "J"}

Answer: 200.376

Prompt: A body of mass 2.3 kg moves at 13.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 13.2^2 and multiply by 0.5 * 2.3.
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=85 degrees through the sine of 2 theta.
3. Substitute v=15.8 m/s and g=9.81 m/s^2.
Final: {"answer": 4.4189, "unit": "m"}

Answer: 4.4189

Prompt: A projectile is launched on level ground with no air resistance at speed 15.8 m/s and angle 85 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=85 degrees through the sine of 2 theta.
Substitute v=15.8 m/s and g=9.81 m/s^2.

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


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1555 * 1.04 * 114.
Final: {"answer": 184360.8, "unit": "J"}

Answer: 184360.8

Prompt: A 1555 g sample has specific heat 1.04 J/(g*K). How much heat is needed to raise its temperature by 114 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1555 * 1.04 * 114.


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=192.2 V and R=70.5 ohm.
Final: {"answer": 523.9835, "unit": "W"}

Answer: 523.9835

Prompt: A resistor has resistance 70.5 ohm and voltage 192.2 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=192.2 V and R=70.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=37.5 mg, t=244 h, and T_half=1.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0, "unit": "mg"}

Answer: 0.0

Prompt: A radioactive sample starts with 37.5 mg. Its half-life is 1.5 hours. How many mg remain after 244 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=37.5 mg, t=244 h, and T_half=1.5 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 = 2.67 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 117.5067, "unit": "g"}

Answer: 117.5067

Prompt: A sample contains 2.67 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 = 2.67 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 1110 mL to 1.11 L.
3. Compute M = 3.04 / 1.11.
Final: {"answer": 2.7387, "unit": "mol/L"}

Answer: 2.7387

Prompt: A solution contains 3.04 mol of solute in 1110 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1110 mL to 1.11 L.
Compute M = 3.04 / 1.11.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.04 y, so each step multiplies y by 1 - h*0.04.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 63.9387, "unit": "state_units"}

Answer: 63.9387

Prompt: Use explicit Euler on dy/dt = -0.04 y with y(0)=78.5, step size h=1.25, for 4 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.04 y, so each step multiplies y by 1 - h*0.04.
Apply that update for 4 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(1.2)=1.28 and f(2.9)=4.51.
3. The interval width is 1.7.
Final: {"answer": 4.9215, "unit": "area_units"}

Answer: 4.9215

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.9x+-1 from x=1.2 to x=2.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.2)=1.28 and f(2.9)=4.51.
The interval width is 1.7.


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=0.18 and add it to the current value.
Final: {"answer": [0.203, 2.087, 1.886], "unit": "temperature_units"}

Answer: 0.203

Answer: 2.087

Answer: 1.886

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=-1.65, right=-0.3; current interior values are [0.05, 2.6, 2.3]. Use r=0.18. 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=0.18 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 4940.0 / 100.
Final: {"answer": 49.4, "unit": "m"}

Answer: 49.4

Prompt: Convert 4940 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 4940.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=27 degrees and keep the unit as newtons.
Final: {"answer": [200.4765, 102.1479], "unit": "N"}

Answer: 200.4765

Answer: 102.1479

Prompt: A vector has magnitude 225 N at 27 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=27 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-8.75, 25.25], "unit": "dimensionless"}

Answer: -8.75

Answer: 25.25

Prompt: A line passes through points (2.5, 3.375) and (6.25, -29.4375). 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 simulation spec case 359339, 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 running_total_002266(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_002266"}

Answer: python_code

Prompt: Write a Python function running_total_002266(values) that returns cumulative sums as a new list. It 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.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 23.4 kg and a = 9.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 228.15, "unit": "N"}

Answer: 228.15

Prompt: A cart has mass 23.4 kg and measured acceleration 9.75 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 = 23.4 kg and a = 9.75 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 = 37.2^2 and multiply by 0.5 * 25.95.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 17955.324, "unit": "J"}

Answer: 17955.324

Prompt: A body of mass 25.95 kg moves at 37.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 37.2^2 and multiply by 0.5 * 25.95.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=47 degrees through the sine of 2 theta.
3. Substitute v=34.9 m/s and g=9.81 m/s^2.
Final: {"answer": 123.8576, "unit": "m"}

Answer: 123.8576

Prompt: A projectile is launched on level ground with no air resistance at speed 34.9 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=34.9 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 = 3.73 * 8.314 * 286 / 91.5.
Final: {"answer": 96.9312, "unit": "kPa"}

Answer: 96.9312

Prompt: An ideal gas sample has n=3.73 mol, T=286 K, and V=91.5 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 = 3.73 * 8.314 * 286 / 91.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 475 * 0.715 * 119.
Final: {"answer": 40415.375, "unit": "J"}

Answer: 40415.375

Prompt: A 475 g sample has specific heat 0.715 J/(g*K). How much heat is needed to raise its temperature by 119 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 475 * 0.715 * 119.


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=35.3 V and R=186.9 ohm.
Final: {"answer": 6.6671, "unit": "W"}

Answer: 6.6671

Prompt: A resistor has resistance 186.9 ohm and voltage 35.3 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=35.3 V and R=186.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=348.5 mg, t=356.5 h, and T_half=113 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 39.1285, "unit": "mg"}

Answer: 39.1285

Prompt: A radioactive sample starts with 348.5 mg. Its half-life is 113 hours. How many mg remain after 356.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=348.5 mg, t=356.5 h, and T_half=113 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 = 0.43 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 43.0374, "unit": "g"}

Answer: 43.0374

Prompt: A sample contains 0.43 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 = 0.43 mol * 100.087 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) = -0.09 y, so each step multiplies y by 1 - h*0.09.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 18.2712, "unit": "state_units"}

Answer: 18.2712

Prompt: Use explicit Euler on dy/dt = -0.09 y with y(0)=20, step size h=0.1, 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) = -0.09 y, so each step multiplies y by 1 - h*0.09.
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(-7.2)=-71.44 and f(-4.5)=-52.
3. The interval width is 2.7.
Final: {"answer": -166.644, "unit": "area_units"}

Answer: -166.644

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.2x+-19.6 from x=-7.2 to x=-4.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.2)=-71.44 and f(-4.5)=-52.
The interval width is 2.7.


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": [0.654, 0.786, 1.778], "unit": "temperature_units"}

Answer: 0.654

Answer: 0.786

Answer: 1.778

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.3, right=2.95; current interior values are [0.45, 0.45, 1.85]. 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 166.0 + 273.15.
Final: {"answer": 439.15, "unit": "K"}

Answer: 439.15

Prompt: Convert 166 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 166.0 + 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=117 degrees and keep the unit as newtons.
Final: {"answer": [-82.8533, 162.6087], "unit": "N"}

Answer: -82.8533

Answer: 162.6087

Prompt: A vector has magnitude 182.5 N at 117 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=117 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": [-8.5, 17.0], "unit": "dimensionless"}

Answer: -8.5

Answer: 17.0

Prompt: A line passes through points (-8, 85) and (-5.5, 63.75). 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 student derivation case 701796, 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 weighted_sum_002284(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_002284"}

Answer: python_code

Prompt: Write a Python function weighted_sum_002284(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

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

try:
    weighted_sum_002284([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 1565 items and budget 36565, 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 = 21.1 kg and a = 6.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 132.93, "unit": "N"}

Answer: 132.93

Prompt: A cart has mass 21.1 kg and measured acceleration 6.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 21.1 kg and a = 6.3 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 42.95^2 and multiply by 0.5 * 21.25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 19599.9641, "unit": "J"}

Answer: 19599.9641

Prompt: A body of mass 21.25 kg moves at 42.95 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 42.95^2 and multiply by 0.5 * 21.25.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=58 degrees through the sine of 2 theta.
3. Substitute v=30.7 m/s and g=9.81 m/s^2.
Final: {"answer": 86.3511, "unit": "m"}

Answer: 86.3511

Prompt: A projectile is launched on level ground with no air resistance at speed 30.7 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=30.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 915 * 3.185 * 28.
Final: {"answer": 81599.7, "unit": "J"}

Answer: 81599.7

Prompt: A 915 g sample has specific heat 3.185 J/(g*K). How much heat is needed to raise its temperature by 28 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 915 * 3.185 * 28.


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=117.6 V and R=113 ohm.
Final: {"answer": 122.3873, "unit": "W"}

Answer: 122.3873

Prompt: A resistor has resistance 113 ohm and voltage 117.6 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=117.6 V and R=113 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=223 mg, t=67 h, and T_half=118 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 150.4461, "unit": "mg"}

Answer: 150.4461

Prompt: A radioactive sample starts with 223 mg. Its half-life is 118 hours. How many mg remain after 67 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=223 mg, t=67 h, and T_half=118 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 = 7.84 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 458.1696, "unit": "g"}

Answer: 458.1696

Prompt: A sample contains 7.84 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 = 7.84 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 3605 mL to 3.605 L.
3. Compute M = 4.77 / 3.605.
Final: {"answer": 1.3232, "unit": "mol/L"}

Answer: 1.3232

Prompt: A solution contains 4.77 mol of solute in 3605 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3605 mL to 3.605 L.
Compute M = 4.77 / 3.605.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 38.3084, "unit": "state_units"}

Answer: 38.3084

Prompt: Use explicit Euler on dy/dt = -0.11 y with y(0)=59, step size h=0.35, 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) = -0.11 y, so each step multiplies y by 1 - h*0.11.
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(3.1)=-8.87 and f(7.2)=-36.34.
3. The interval width is 4.1.
Final: {"answer": -92.6805, "unit": "area_units"}

Answer: -92.6805

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.7x+11.9 from x=3.1 to x=7.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3.1)=-8.87 and f(7.2)=-36.34.
The interval width is 4.1.


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=0.34 and add it to the current value.
Final: {"answer": [0.515, -0.483, -0.342], "unit": "temperature_units"}

Answer: 0.515

Answer: -0.483

Answer: -0.342

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=2.3, right=1.05; current interior values are [0.6, -1.35, -0.75]. Use r=0.34. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -70.5 + 273.15.
Final: {"answer": 202.65, "unit": "K"}

Answer: 202.65

Prompt: Convert -70.5 degC to K. Return the converted value with unit.

Kelvin equals Celsius plus 273.15.
Apply the conversion factor directly to the given value.
Compute -70.5 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=96 degrees and keep the unit as newtons.
Final: {"answer": [-17.404, 165.5879], "unit": "N"}

Answer: -17.404

Answer: 165.5879

Prompt: A vector has magnitude 166.5 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": [9.05, -3.25], "unit": "dimensionless"}

Answer: 9.05

Answer: -3.25

Prompt: A line passes through points (17, 150.6) and (25.25, 225.263). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In simulation spec case 256505, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. 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 running_total_002302(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_002302"}

Answer: python_code

Prompt: Write a Python function running_total_002302(values) that returns cumulative sums as a new list. It 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.


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=2.84 mol and T=380 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 = 1.85 kg and a = 8.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 15.725, "unit": "N"}

Answer: 15.725

Prompt: A cart has mass 1.85 kg and measured acceleration 8.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 1.85 kg and a = 8.5 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 36.65^2 and multiply by 0.5 * 27.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 18704.3733, "unit": "J"}

Answer: 18704.3733

Prompt: A body of mass 27.85 kg moves at 36.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 36.65^2 and multiply by 0.5 * 27.85.
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=30 degrees through the sine of 2 theta.
3. Substitute v=27.4 m/s and g=9.81 m/s^2.
Final: {"answer": 66.277, "unit": "m"}

Answer: 66.277

Prompt: A projectile is launched on level ground with no air resistance at speed 27.4 m/s and angle 30 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=30 degrees through the sine of 2 theta.
Substitute v=27.4 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.44 * 8.314 * 544 / 111.9.
Final: {"answer": 98.6208, "unit": "kPa"}

Answer: 98.6208

Prompt: An ideal gas sample has n=2.44 mol, T=544 K, and V=111.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.44 * 8.314 * 544 / 111.9.


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=142.7 V and R=78.7 ohm.
Final: {"answer": 258.7457, "unit": "W"}

Answer: 258.7457

Prompt: A resistor has resistance 78.7 ohm and voltage 142.7 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=142.7 V and R=78.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=919 mg, t=24.5 h, and T_half=71 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 723.5007, "unit": "mg"}

Answer: 723.5007

Prompt: A radioactive sample starts with 919 mg. Its half-life is 71 hours. How many mg remain after 24.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=919 mg, t=24.5 h, and T_half=71 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.28 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 367.0032, "unit": "g"}

Answer: 367.0032

Prompt: A sample contains 6.28 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 = 6.28 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-7.6)=39.88 and f(-3.9)=23.97.
3. The interval width is 3.7.
Final: {"answer": 118.1225, "unit": "area_units"}

Answer: 118.1225

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.3x+7.2 from x=-7.6 to x=-3.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.6)=39.88 and f(-3.9)=23.97.
The interval width is 3.7.


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=0.28 and add it to the current value.
Final: {"answer": [0.926, 0.858, 0.02], "unit": "temperature_units"}

Answer: 0.926

Answer: 0.858

Answer: 0.02

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=-0.85, right=0; current interior values are [1.85, 1.25, -0.75]. Use r=0.28. 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=0.28 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=247 degrees and keep the unit as newtons.
Final: {"answer": [-8.4007, -19.7909], "unit": "N"}

Answer: -8.4007

Answer: -19.7909

Prompt: A vector has magnitude 21.5 N at 247 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=247 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-7.3, 11.25], "unit": "dimensionless"}

Answer: -7.3

Answer: 11.25

Prompt: A line passes through points (4, -17.95) and (14.75, -96.425). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In student derivation case 226755, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def finite_differences_002320(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_002320"}

Answer: python_code

Prompt: Write a Python function finite_differences_002320(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_002320([5]) == []

assert finite_differences_002320([]) == []


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 segmentation scoring problem with 3183 items and budget 51285, 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 = 9.6 kg and a = 11.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 109.92, "unit": "N"}

Answer: 109.92

Prompt: A cart has mass 9.6 kg and measured acceleration 11.45 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 = 9.6 kg and a = 11.45 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 = 34.15^2 and multiply by 0.5 * 10.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 6035.2014, "unit": "J"}

Answer: 6035.2014

Prompt: A body of mass 10.35 kg moves at 34.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 34.15^2 and multiply by 0.5 * 10.35.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=8 degrees through the sine of 2 theta.
3. Substitute v=60.2 m/s and g=9.81 m/s^2.
Final: {"answer": 101.8268, "unit": "m"}

Answer: 101.8268

Prompt: A projectile is launched on level ground with no air resistance at speed 60.2 m/s and angle 8 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=8 degrees through the sine of 2 theta.
Substitute v=60.2 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 = 0.38 * 8.314 * 256 / 2.9.
Final: {"answer": 278.8917, "unit": "kPa"}

Answer: 278.8917

Prompt: An ideal gas sample has n=0.38 mol, T=256 K, and V=2.9 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 = 0.38 * 8.314 * 256 / 2.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1355 * 4.335 * 115.
Final: {"answer": 675501.375, "unit": "J"}

Answer: 675501.375

Prompt: A 1355 g sample has specific heat 4.335 J/(g*K). How much heat is needed to raise its temperature by 115 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1355 * 4.335 * 115.


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=43.9 V and R=16.2 ohm.
Final: {"answer": 118.9636, "unit": "W"}

Answer: 118.9636

Prompt: A resistor has resistance 16.2 ohm and voltage 43.9 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=43.9 V and R=16.2 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.66 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 155.4504, "unit": "g"}

Answer: 155.4504

Prompt: A sample contains 2.66 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 = 2.66 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 3090 mL to 3.09 L.
3. Compute M = 3.155 / 3.09.
Final: {"answer": 1.021, "unit": "mol/L"}

Answer: 1.021

Prompt: A solution contains 3.155 mol of solute in 3090 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3090 mL to 3.09 L.
Compute M = 3.155 / 3.09.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.24 y, so each step multiplies y by 1 - h*0.24.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 0.1079, "unit": "state_units"}

Answer: 0.1079

Prompt: Use explicit Euler on dy/dt = -0.24 y with y(0)=18, step size h=1.55, 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) = -0.24 y, so each step multiplies y by 1 - h*0.24.
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=0.32 and add it to the current value.
Final: {"answer": [1.8, 0.958, 0.754], "unit": "temperature_units"}

Answer: 1.8

Answer: 0.958

Answer: 0.754

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=2.3, right=2.35; current interior values are [3.0, -0.05, 0.05]. Use r=0.32. 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=0.32 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=182 degrees and keep the unit as newtons.
Final: {"answer": [-254.345, -8.8819], "unit": "N"}

Answer: -254.345

Answer: -8.8819

Prompt: A vector has magnitude 254.5 N at 182 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=182 degrees and keep the unit as newtons.


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

Answer: consistent

Prompt: In student derivation case 173257, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def normalize_002338(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_002338"}

Answer: python_code

Prompt: Write a Python function normalize_002338(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_002338([2, 3, 5]); assert len(out) == 3

try:
    normalize_002338([1, -1])
    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: rate_constant, number_of_steps.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=61.5 and h=1.9, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 9.15 kg and a = 10.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 95.6175, "unit": "N"}

Answer: 95.6175

Prompt: A cart has mass 9.15 kg and measured acceleration 10.45 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 = 9.15 kg and a = 10.45 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 = 11.85^2 and multiply by 0.5 * 23.95.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1681.5594, "unit": "J"}

Answer: 1681.5594

Prompt: A body of mass 23.95 kg moves at 11.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 11.85^2 and multiply by 0.5 * 23.95.
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 = 2.37 * 8.314 * 530 / 23.0.
Final: {"answer": 454.0528, "unit": "kPa"}

Answer: 454.0528

Prompt: An ideal gas sample has n=2.37 mol, T=530 K, and V=23.0 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 = 2.37 * 8.314 * 530 / 23.0.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=214.7 V and R=191.8 ohm.
Final: {"answer": 240.3342, "unit": "W"}

Answer: 240.3342

Prompt: A resistor has resistance 191.8 ohm and voltage 214.7 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=214.7 V and R=191.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=856.5 mg, t=34.5 h, and T_half=96.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 668.5059, "unit": "mg"}

Answer: 668.5059

Prompt: A radioactive sample starts with 856.5 mg. Its half-life is 96.5 hours. How many mg remain after 34.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=856.5 mg, t=34.5 h, and T_half=96.5 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 = 5.42 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 97.6413, "unit": "g"}

Answer: 97.6413

Prompt: A sample contains 5.42 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 = 5.42 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 2925 mL to 2.925 L.
3. Compute M = 3.52 / 2.925.
Final: {"answer": 1.2034, "unit": "mol/L"}

Answer: 1.2034

Prompt: A solution contains 3.52 mol of solute in 2925 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2925 mL to 2.925 L.
Compute M = 3.52 / 2.925.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(8.4)=73.06 and f(11.6)=95.14.
3. The interval width is 3.2.
Final: {"answer": 269.12, "unit": "area_units"}

Answer: 269.12

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.9x+15.1 from x=8.4 to x=11.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(8.4)=73.06 and f(11.6)=95.14.
The interval width is 3.2.


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=0.06 and add it to the current value.
Final: {"answer": [1.584, 2.691, 1.391], "unit": "temperature_units"}

Answer: 1.584

Answer: 2.691

Answer: 1.391

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=-0.65, right=-0.2; current interior values are [1.65, 2.85, 1.4]. 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 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 45789.0 / 1000.
Final: {"answer": 45.789, "unit": "kg"}

Answer: 45.789

Prompt: Convert 45789 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 45789.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=5 degrees and keep the unit as newtons.
Final: {"answer": [405.4512, 35.4724], "unit": "N"}

Answer: 405.4512

Answer: 35.4724

Prompt: A vector has magnitude 407 N at 5 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=5 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": [-6.7, 29.5], "unit": "dimensionless"}

Answer: -6.7

Answer: 29.5

Prompt: A line passes through points (-17.75, 148.425) and (-7.75, 81.425). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In simulation spec case 431345, 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
import math

def unit_vector_002356(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_002356"}

Answer: python_code

Prompt: Write a Python function unit_vector_002356(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_002356(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=2.92 mol and T=597 K, but does not give volume. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=54 degrees through the sine of 2 theta.
3. Substitute v=74.5 m/s and g=9.81 m/s^2.
Final: {"answer": 538.0837, "unit": "m"}

Answer: 538.0837

Prompt: A projectile is launched on level ground with no air resistance at speed 74.5 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=74.5 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.83 * 8.314 * 581 / 73.8.
Final: {"answer": 119.7791, "unit": "kPa"}

Answer: 119.7791

Prompt: An ideal gas sample has n=1.83 mol, T=581 K, and V=73.8 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 = 1.83 * 8.314 * 581 / 73.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 670 * 1.49 * 77.
Final: {"answer": 76869.1, "unit": "J"}

Answer: 76869.1

Prompt: A 670 g sample has specific heat 1.49 J/(g*K). How much heat is needed to raise its temperature by 77 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 670 * 1.49 * 77.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=51 V and R=48.6 ohm.
Final: {"answer": 53.5185, "unit": "W"}

Answer: 53.5185

Prompt: A resistor has resistance 48.6 ohm and voltage 51 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=51 V and R=48.6 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=815.5 mg, t=258.5 h, and T_half=79.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 85.6255, "unit": "mg"}

Answer: 85.6255

Prompt: A radioactive sample starts with 815.5 mg. Its half-life is 79.5 hours. How many mg remain after 258.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=815.5 mg, t=258.5 h, and T_half=79.5 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 = 5.92 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1066.5235, "unit": "g"}

Answer: 1066.5235

Prompt: A sample contains 5.92 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.92 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6)=47.5 and f(2.6)=-0.66.
3. The interval width is 8.6.
Final: {"answer": 201.412, "unit": "area_units"}

Answer: 201.412

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.6x+13.9 from x=-6 to x=2.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6)=47.5 and f(2.6)=-0.66.
The interval width is 8.6.


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=0.4 and add it to the current value.
Final: {"answer": [0.71, 0.36, -1.45], "unit": "temperature_units"}

Answer: 0.71

Answer: 0.36

Answer: -1.45

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=1.95, right=-1.45; current interior values are [2.85, -1.6, -1.15]. 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. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 13863.0 / 1000.
Final: {"answer": 13.863, "unit": "kg"}

Answer: 13.863

Prompt: Convert 13863 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 13863.0 / 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": [171.8636, 184.3011], "unit": "N"}

Answer: 171.8636

Answer: 184.3011

Prompt: A vector has magnitude 252 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": [-2.0, 13.0], "unit": "dimensionless"}

Answer: -2.0

Answer: 13.0

Prompt: A line passes through points (9, -5) and (23.25, -33.5). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In quality-control check case 152041, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. 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 segmentation scoring problem with 459 items and budget 53210, 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 = 24.2 kg and a = 5.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 141.57, "unit": "N"}

Answer: 141.57

Prompt: A cart has mass 24.2 kg and measured acceleration 5.85 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 = 24.2 kg and a = 5.85 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 = 2.2^2 and multiply by 0.5 * 11.55.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 27.951, "unit": "J"}

Answer: 27.951

Prompt: A body of mass 11.55 kg moves at 2.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 2.2^2 and multiply by 0.5 * 11.55.
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=43 degrees through the sine of 2 theta.
3. Substitute v=58.1 m/s and g=9.81 m/s^2.
Final: {"answer": 343.2607, "unit": "m"}

Answer: 343.2607

Prompt: A projectile is launched on level ground with no air resistance at speed 58.1 m/s and angle 43 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=43 degrees through the sine of 2 theta.
Substitute v=58.1 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 = 4.86 * 8.314 * 526 / 90.3.
Final: {"answer": 235.3663, "unit": "kPa"}

Answer: 235.3663

Prompt: An ideal gas sample has n=4.86 mol, T=526 K, and V=90.3 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 = 4.86 * 8.314 * 526 / 90.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 780 * 3.965 * 106.
Final: {"answer": 327826.2, "unit": "J"}

Answer: 327826.2

Prompt: A 780 g sample has specific heat 3.965 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 = 780 * 3.965 * 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=188.3 V and R=93 ohm.
Final: {"answer": 381.2569, "unit": "W"}

Answer: 381.2569

Prompt: A resistor has resistance 93 ohm and voltage 188.3 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=188.3 V and R=93 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=745 mg, t=170.5 h, and T_half=96 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 217.5276, "unit": "mg"}

Answer: 217.5276

Prompt: A radioactive sample starts with 745 mg. Its half-life is 96 hours. How many mg remain after 170.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=745 mg, t=170.5 h, and T_half=96 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 4920 mL to 4.92 L.
3. Compute M = 0.8 / 4.92.
Final: {"answer": 0.1626, "unit": "mol/L"}

Answer: 0.1626

Prompt: A solution contains 0.8 mol of solute in 4920 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4920 mL to 4.92 L.
Compute M = 0.8 / 4.92.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.93 y, so each step multiplies y by 1 - h*0.93.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": -0.0059, "unit": "state_units"}

Answer: -0.0059

Prompt: Use explicit Euler on dy/dt = -0.93 y with y(0)=78, step size h=1.45, 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) = -0.93 y, so each step multiplies y by 1 - h*0.93.
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(-2.6)=7.02 and f(0)=2.6.
3. The interval width is 2.6.
Final: {"answer": 12.506, "unit": "area_units"}

Answer: 12.506

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.7x+2.6 from x=-2.6 to x=0. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-2.6)=7.02 and f(0)=2.6.
The interval width is 2.6.


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=0.36 and add it to the current value.
Final: {"answer": [0.556, 0.534, -0.454], "unit": "temperature_units"}

Answer: 0.556

Answer: 0.534

Answer: -0.454

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=1.2, right=0.65; current interior values are [2.95, -1.95, 0.05]. Use r=0.36. 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=0.36 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 139.5 + 273.15.
Final: {"answer": 412.65, "unit": "K"}

Answer: 412.65

Prompt: Convert 139.5 degC to K. Return the converted value with unit.

Kelvin equals Celsius plus 273.15.
Apply the conversion factor directly to the given value.
Compute 139.5 + 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": [9.05, 29.5], "unit": "dimensionless"}

Answer: 9.05

Answer: 29.5

Prompt: A line passes through points (18, 192.4) and (25.25, 258.013). 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 817110, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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=4.2 mol and T=550 K, but does not give volume. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 10.6 kg and a = 1.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 15.37, "unit": "N"}

Answer: 15.37

Prompt: A cart has mass 10.6 kg and measured acceleration 1.45 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 = 10.6 kg and a = 1.45 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 = 39.45^2 and multiply by 0.5 * 0.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 661.4286, "unit": "J"}

Answer: 661.4286

Prompt: A body of mass 0.85 kg moves at 39.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 39.45^2 and multiply by 0.5 * 0.85.
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 = 2.59 * 8.314 * 515 / 16.3.
Final: {"answer": 680.3453, "unit": "kPa"}

Answer: 680.3453

Prompt: An ideal gas sample has n=2.59 mol, T=515 K, and V=16.3 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 = 2.59 * 8.314 * 515 / 16.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 935 * 2.44 * 33.
Final: {"answer": 75286.2, "unit": "J"}

Answer: 75286.2

Prompt: A 935 g sample has specific heat 2.44 J/(g*K). How much heat is needed to raise its temperature by 33 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 935 * 2.44 * 33.


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=173.1 V and R=142.1 ohm.
Final: {"answer": 210.8628, "unit": "W"}

Answer: 210.8628

Prompt: A resistor has resistance 142.1 ohm and voltage 173.1 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=173.1 V and R=142.1 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.89 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 16.0334, "unit": "g"}

Answer: 16.0334

Prompt: A sample contains 0.89 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 = 0.89 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 3055 mL to 3.055 L.
3. Compute M = 2.515 / 3.055.
Final: {"answer": 0.8232, "unit": "mol/L"}

Answer: 0.8232

Prompt: A solution contains 2.515 mol of solute in 3055 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3055 mL to 3.055 L.
Compute M = 2.515 / 3.055.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-8.1)=-9.05 and f(-2.2)=-12.
3. The interval width is 5.9.
Final: {"answer": -62.0975, "unit": "area_units"}

Answer: -62.0975

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.5x+-13.1 from x=-8.1 to x=-2.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-8.1)=-9.05 and f(-2.2)=-12.
The interval width is 5.9.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.22 and add it to the current value.
Final: {"answer": [0.212, 0.068, 0.507], "unit": "temperature_units"}

Answer: 0.212

Answer: 0.068

Answer: 0.507

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=-1.7, right=0.15; current interior values are [1.4, -0.9, 1.2]. Use r=0.22. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 2861.0 / 100.
Final: {"answer": 28.61, "unit": "m"}

Answer: 28.61

Prompt: Convert 2861 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 2861.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=324 degrees and keep the unit as newtons.
Final: {"answer": [81.3062, -59.0724], "unit": "N"}

Answer: 81.3062

Answer: -59.0724

Prompt: A vector has magnitude 100.5 N at 324 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=324 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": [1.7, 4.0], "unit": "dimensionless"}

Answer: 1.7

Answer: 4.0

Prompt: A line passes through points (4.25, 11.225) and (17.5, 33.75). 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 519891, 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 normalize_002410(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_002410"}

Answer: python_code

Prompt: Write a Python function normalize_002410(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_002410([2, 3, 5]); assert len(out) == 3

try:
    normalize_002410([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 2.55 kg and a = 5.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 14.025, "unit": "N"}

Answer: 14.025

Prompt: A cart has mass 2.55 kg and measured acceleration 5.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 2.55 kg and a = 5.5 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 43.1^2 and multiply by 0.5 * 15.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 13978.5153, "unit": "J"}

Answer: 13978.5153

Prompt: A body of mass 15.05 kg moves at 43.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 43.1^2 and multiply by 0.5 * 15.05.
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=69 degrees through the sine of 2 theta.
3. Substitute v=51.2 m/s and g=9.81 m/s^2.
Final: {"answer": 178.8059, "unit": "m"}

Answer: 178.8059

Prompt: A projectile is launched on level ground with no air resistance at speed 51.2 m/s and angle 69 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=69 degrees through the sine of 2 theta.
Substitute v=51.2 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1745 * 4.75 * 67.
Final: {"answer": 555346.25, "unit": "J"}

Answer: 555346.25

Prompt: A 1745 g sample has specific heat 4.75 J/(g*K). How much heat is needed to raise its temperature by 67 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1745 * 4.75 * 67.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=643.5 mg, t=181.5 h, and T_half=55.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 66.6959, "unit": "mg"}

Answer: 66.6959

Prompt: A radioactive sample starts with 643.5 mg. Its half-life is 55.5 hours. How many mg remain after 181.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=643.5 mg, t=181.5 h, and T_half=55.5 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 745 mL to 0.745 L.
3. Compute M = 4.64 / 0.745.
Final: {"answer": 6.2282, "unit": "mol/L"}

Answer: 6.2282

Prompt: A solution contains 4.64 mol of solute in 745 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 745 mL to 0.745 L.
Compute M = 4.64 / 0.745.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.84 y, so each step multiplies y by 1 - h*0.84.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.84 y with y(0)=69, step size h=0.9, 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) = -0.84 y, so each step multiplies y by 1 - h*0.84.
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=0.04 and add it to the current value.
Final: {"answer": [1.752, 1.3, 2.858], "unit": "temperature_units"}

Answer: 1.752

Answer: 1.3

Answer: 2.858

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=-1.1, right=1.25; current interior values are [1.9, 1.2, 3.0]. Use r=0.04. 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=0.04 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 1412.0 / 1000.
Final: {"answer": 1.412, "unit": "kg"}

Answer: 1.412

Prompt: Convert 1412 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 1412.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=290 degrees and keep the unit as newtons.
Final: {"answer": [66.6939, -183.2401], "unit": "N"}

Answer: 66.6939

Answer: -183.2401

Prompt: A vector has magnitude 195 N at 290 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=290 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": [-8.7, 4.25], "unit": "dimensionless"}

Answer: -8.7

Answer: 4.25

Prompt: A line passes through points (17.25, -145.825) and (29.75, -254.575). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In model card equation case 481371, 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: left_boundary, right_boundary.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.32 and interior values [-1.1, -0.35, -1.7], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 1.15 kg and a = 15.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 17.365, "unit": "N"}

Answer: 17.365

Prompt: A cart has mass 1.15 kg and measured acceleration 15.1 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 = 1.15 kg and a = 15.1 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 = 17^2 and multiply by 0.5 * 12.45.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1799.025, "unit": "J"}

Answer: 1799.025

Prompt: A body of mass 12.45 kg moves at 17 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 17^2 and multiply by 0.5 * 12.45.
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 = 2.97 * 8.314 * 526 / 31.6.
Final: {"answer": 411.0221, "unit": "kPa"}

Answer: 411.0221

Prompt: An ideal gas sample has n=2.97 mol, T=526 K, and V=31.6 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 = 2.97 * 8.314 * 526 / 31.6.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=222.5 mg, t=260.5 h, and T_half=109 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 42.4518, "unit": "mg"}

Answer: 42.4518

Prompt: A radioactive sample starts with 222.5 mg. Its half-life is 109 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=222.5 mg, t=260.5 h, and T_half=109 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) = -0.91 y, so each step multiplies y by 1 - h*0.91.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 0.0521, "unit": "state_units"}

Answer: 0.0521

Prompt: Use explicit Euler on dy/dt = -0.91 y with y(0)=35, step size h=0.8, 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) = -0.91 y, so each step multiplies y by 1 - h*0.91.
Apply that update for 5 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)=-22 and f(9.1)=-69.25.
3. The interval width is 6.3.
Final: {"answer": -287.4375, "unit": "area_units"}

Answer: -287.4375

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.5x+-1 from x=2.8 to x=9.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(2.8)=-22 and f(9.1)=-69.25.
The interval width is 6.3.


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": [2.075, 0.277, 1.403], "unit": "temperature_units"}

Answer: 2.075

Answer: 0.277

Answer: 1.403

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=2.8, right=1.8; current interior values are [1.5, 1.45, -1.15]. 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 44815.0 / 1000.
Final: {"answer": 44.815, "unit": "kg"}

Answer: 44.815

Prompt: Convert 44815 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 44815.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=152 degrees and keep the unit as newtons.
Final: {"answer": [-310.7976, 165.254], "unit": "N"}

Answer: -310.7976

Answer: 165.254

Prompt: A vector has magnitude 352 N at 152 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=152 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-2.9, 30.0], "unit": "dimensionless"}

Answer: -2.9

Answer: 30.0

Prompt: A line passes through points (-1.25, 33.625) and (9, 3.9). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In field worksheet case 797531, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def weighted_sum_002446(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_002446"}

Answer: python_code

Prompt: Write a Python function weighted_sum_002446(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

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

try:
    weighted_sum_002446([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=1.04 mol and T=369 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. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 19.9^2 and multiply by 0.5 * 8.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1752.3442, "unit": "J"}

Answer: 1752.3442

Prompt: A body of mass 8.85 kg moves at 19.9 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 19.9^2 and multiply by 0.5 * 8.85.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=7 degrees through the sine of 2 theta.
3. Substitute v=43.4 m/s and g=9.81 m/s^2.
Final: {"answer": 46.45, "unit": "m"}

Answer: 46.45

Prompt: A projectile is launched on level ground with no air resistance at speed 43.4 m/s and angle 7 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=7 degrees through the sine of 2 theta.
Substitute v=43.4 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.19 * 8.314 * 315 / 6.5.
Final: {"answer": 1285.2804, "unit": "kPa"}

Answer: 1285.2804

Prompt: An ideal gas sample has n=3.19 mol, T=315 K, and V=6.5 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 = 3.19 * 8.314 * 315 / 6.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 920 * 2.85 * 115.
Final: {"answer": 301530.0, "unit": "J"}

Answer: 301530.0

Prompt: A 920 g sample has specific heat 2.85 J/(g*K). How much heat is needed to raise its temperature by 115 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 920 * 2.85 * 115.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=93.8 V and R=120.9 ohm.
Final: {"answer": 72.7745, "unit": "W"}

Answer: 72.7745

Prompt: A resistor has resistance 120.9 ohm and voltage 93.8 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=93.8 V and R=120.9 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.02 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 702.6107, "unit": "g"}

Answer: 702.6107

Prompt: A sample contains 7.02 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.02 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 3730 mL to 3.73 L.
3. Compute M = 2.46 / 3.73.
Final: {"answer": 0.6595, "unit": "mol/L"}

Answer: 0.6595

Prompt: A solution contains 2.46 mol of solute in 3730 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3730 mL to 3.73 L.
Compute M = 2.46 / 3.73.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.26 y, so each step multiplies y by 1 - h*0.26.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 10.7577, "unit": "state_units"}

Answer: 10.7577

Prompt: Use explicit Euler on dy/dt = -0.26 y with y(0)=14, step size h=0.1, 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) = -0.26 y, so each step multiplies y by 1 - h*0.26.
Apply that update for 10 steps and round the final state.