Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 23.65^2 and multiply by 0.5 * 15.25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 4264.8341, "unit": "J"}

Answer: 4264.8341

Prompt: A body of mass 15.25 kg moves at 23.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 23.65^2 and multiply by 0.5 * 15.25.
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=6 degrees through the sine of 2 theta.
3. Substitute v=59.9 m/s and g=9.81 m/s^2.
Final: {"answer": 76.0438, "unit": "m"}

Answer: 76.0438

Prompt: A projectile is launched on level ground with no air resistance at speed 59.9 m/s and angle 6 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=6 degrees through the sine of 2 theta.
Substitute v=59.9 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 = 1780 * 2.19 * 97.
Final: {"answer": 378125.4, "unit": "J"}

Answer: 378125.4

Prompt: A 1780 g sample has specific heat 2.19 J/(g*K). How much heat is needed to raise its temperature by 97 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1780 * 2.19 * 97.


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=126.4 V and R=94.8 ohm.
Final: {"answer": 168.5333, "unit": "W"}

Answer: 168.5333

Prompt: A resistor has resistance 94.8 ohm and voltage 126.4 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=126.4 V and R=94.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=888 mg, t=272.5 h, and T_half=14.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.002, "unit": "mg"}

Answer: 0.002

Prompt: A radioactive sample starts with 888 mg. Its half-life is 14.5 hours. How many mg remain after 272.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=888 mg, t=272.5 h, and T_half=14.5 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 = 1.07 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 192.7669, "unit": "g"}

Answer: 192.7669

Prompt: A sample contains 1.07 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.07 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 3520 mL to 3.52 L.
3. Compute M = 2.93 / 3.52.
Final: {"answer": 0.8324, "unit": "mol/L"}

Answer: 0.8324

Prompt: A solution contains 2.93 mol of solute in 3520 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3520 mL to 3.52 L.
Compute M = 2.93 / 3.52.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.29 y, so each step multiplies y by 1 - h*0.29.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 3.5194, "unit": "state_units"}

Answer: 3.5194

Prompt: Use explicit Euler on dy/dt = -0.29 y with y(0)=54.5, step size h=1, for 8 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.29 y, so each step multiplies y by 1 - h*0.29.
Apply that update for 8 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(8.5)=77.65 and f(11.1)=96.11.
3. The interval width is 2.6.
Final: {"answer": 225.888, "unit": "area_units"}

Answer: 225.888

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.1x+17.3 from x=8.5 to x=11.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(8.5)=77.65 and f(11.1)=96.11.
The interval width is 2.6.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=273 degrees and keep the unit as newtons.
Final: {"answer": [22.426, -427.9128], "unit": "N"}

Answer: 22.426

Answer: -427.9128

Prompt: A vector has magnitude 428.5 N at 273 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=273 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": [0.3, 19.25], "unit": "dimensionless"}

Answer: 0.3

Answer: 19.25

Prompt: A line passes through points (17.25, 24.425) and (19.25, 25.025). 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 model card equation case 67694, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def weighted_sum_004012(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_004012"}

Answer: python_code

Prompt: Write a Python function weighted_sum_004012(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_004012([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=0.56 mol and T=319 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 = 9.9 kg and a = 9.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 92.07, "unit": "N"}

Answer: 92.07

Prompt: A cart has mass 9.9 kg and measured acceleration 9.3 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 = 9.9 kg and a = 9.3 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 = 18.65^2 and multiply by 0.5 * 12.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2113.0217, "unit": "J"}

Answer: 2113.0217

Prompt: A body of mass 12.15 kg moves at 18.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 18.65^2 and multiply by 0.5 * 12.15.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1770 * 0.905 * 52.
Final: {"answer": 83296.2, "unit": "J"}

Answer: 83296.2

Prompt: A 1770 g sample has specific heat 0.905 J/(g*K). How much heat is needed to raise its temperature by 52 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1770 * 0.905 * 52.


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=103.2 V and R=177.6 ohm.
Final: {"answer": 59.9676, "unit": "W"}

Answer: 59.9676

Prompt: A resistor has resistance 177.6 ohm and voltage 103.2 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=103.2 V and R=177.6 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.62 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 247.3362, "unit": "g"}

Answer: 247.3362

Prompt: A sample contains 5.62 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.62 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 4960 mL to 4.96 L.
3. Compute M = 0.805 / 4.96.
Final: {"answer": 0.1623, "unit": "mol/L"}

Answer: 0.1623

Prompt: A solution contains 0.805 mol of solute in 4960 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4960 mL to 4.96 L.
Compute M = 0.805 / 4.96.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.49 y, so each step multiplies y by 1 - h*0.49.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.5855, "unit": "state_units"}

Answer: 0.5855

Prompt: Use explicit Euler on dy/dt = -0.49 y with y(0)=61, step size h=1.1, 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) = -0.49 y, so each step multiplies y by 1 - h*0.49.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.34 and add it to the current value.
Final: {"answer": [1.393, 0.088, 0.841], "unit": "temperature_units"}

Answer: 1.393

Answer: 0.088

Answer: 0.841

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=2.5, right=2.1; current interior values are [0.05, 1.55, -1.25]. Use r=0.34. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3200.0 / 100.
Final: {"answer": 32.0, "unit": "m"}

Answer: 32.0

Prompt: Convert 3200 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 3200.0 / 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": [240.5718, 122.5774], "unit": "N"}

Answer: 240.5718

Answer: 122.5774

Prompt: A vector has magnitude 270 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. Compare the dimensions on both sides of the equation.
2. volt squared divided by ohm is watt
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In quality-control check case 426930, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
volt squared divided by ohm is watt
The equation is valid only if both sides have identical dimensions.

Answer: consistent


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

```python
def threshold_flags_004030(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_004030"}

Answer: python_code

Prompt: Write a Python function threshold_flags_004030(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.

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

assert threshold_flags_004030([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_004030([], 5) == []

assert threshold_flags_004030([-1, 0], 0) == [False, True]


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=5.59 mol and T=490 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 = 22.15 kg and a = 13.05 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 289.0575, "unit": "N"}

Answer: 289.0575

Prompt: A cart has mass 22.15 kg and measured acceleration 13.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 22.15 kg and a = 13.05 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 9.4^2 and multiply by 0.5 * 24.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1060.32, "unit": "J"}

Answer: 1060.32

Prompt: A body of mass 24 kg moves at 9.4 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 9.4^2 and multiply by 0.5 * 24.
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=9 degrees through the sine of 2 theta.
3. Substitute v=30.8 m/s and g=9.81 m/s^2.
Final: {"answer": 29.8824, "unit": "m"}

Answer: 29.8824

Prompt: A projectile is launched on level ground with no air resistance at speed 30.8 m/s and angle 9 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=9 degrees through the sine of 2 theta.
Substitute v=30.8 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 605 * 4.095 * 94.
Final: {"answer": 232882.65, "unit": "J"}

Answer: 232882.65

Prompt: A 605 g sample has specific heat 4.095 J/(g*K). How much heat is needed to raise its temperature by 94 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 605 * 4.095 * 94.


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=78.4 V and R=82.1 ohm.
Final: {"answer": 74.8667, "unit": "W"}

Answer: 74.8667

Prompt: A resistor has resistance 82.1 ohm and voltage 78.4 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=78.4 V and R=82.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=790 mg, t=154.5 h, and T_half=53 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 104.7361, "unit": "mg"}

Answer: 104.7361

Prompt: A radioactive sample starts with 790 mg. Its half-life is 53 hours. How many mg remain after 154.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=790 mg, t=154.5 h, and T_half=53 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 = 5.57 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 557.4846, "unit": "g"}

Answer: 557.4846

Prompt: A sample contains 5.57 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.57 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 185 mL to 0.185 L.
3. Compute M = 0.525 / 0.185.
Final: {"answer": 2.8378, "unit": "mol/L"}

Answer: 2.8378

Prompt: A solution contains 0.525 mol of solute in 185 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 185 mL to 0.185 L.
Compute M = 0.525 / 0.185.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.79 y, so each step multiplies y by 1 - h*0.79.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.79 y with y(0)=20.5, step size h=1.35, for 12 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.79 y, so each step multiplies y by 1 - h*0.79.
Apply that update for 12 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.12 and add it to the current value.
Final: {"answer": [0.052, -1.246, -1.632], "unit": "temperature_units"}

Answer: 0.052

Answer: -1.246

Answer: -1.632

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=3, right=0.05; current interior values are [-0.2, -1.3, -1.95]. Use r=0.12. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.12 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4327.5 / 100.
Final: {"answer": 43.275, "unit": "m"}

Answer: 43.275

Prompt: Convert 4327.5 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 4327.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=134 degrees and keep the unit as newtons.
Final: {"answer": [-297.3138, 307.8774], "unit": "N"}

Answer: -297.3138

Answer: 307.8774

Prompt: A vector has magnitude 428 N at 134 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=134 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": [1.65, -24.0], "unit": "dimensionless"}

Answer: 1.65

Answer: -24.0

Prompt: A line passes through points (0, -24) and (1.5, -21.525). 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 simulation spec case 637547, 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_004048(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_004048"}

Answer: python_code

Prompt: Write a Python function weighted_sum_004048(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_004048([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: target_schema, valid_examples.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each mobile clinical record from batch 406004 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 10.45 kg and a = 3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 31.35, "unit": "N"}

Answer: 31.35

Prompt: A cart has mass 10.45 kg and measured acceleration 3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 10.45 kg and a = 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 = 3.45^2 and multiply by 0.5 * 13.4.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 79.7468, "unit": "J"}

Answer: 79.7468

Prompt: A body of mass 13.4 kg moves at 3.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 3.45^2 and multiply by 0.5 * 13.4.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=78 degrees through the sine of 2 theta.
3. Substitute v=56.7 m/s and g=9.81 m/s^2.
Final: {"answer": 133.2939, "unit": "m"}

Answer: 133.2939

Prompt: A projectile is launched on level ground with no air resistance at speed 56.7 m/s and angle 78 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=78 degrees through the sine of 2 theta.
Substitute v=56.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.22 * 8.314 * 584 / 25.7.
Final: {"answer": 608.3389, "unit": "kPa"}

Answer: 608.3389

Prompt: An ideal gas sample has n=3.22 mol, T=584 K, and V=25.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.22 * 8.314 * 584 / 25.7.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=34.2 V and R=58.9 ohm.
Final: {"answer": 19.8581, "unit": "W"}

Answer: 19.8581

Prompt: A resistor has resistance 58.9 ohm and voltage 34.2 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=34.2 V and R=58.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=657.5 mg, t=202.5 h, and T_half=29.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 5.6429, "unit": "mg"}

Answer: 5.6429

Prompt: A radioactive sample starts with 657.5 mg. Its half-life is 29.5 hours. How many mg remain after 202.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=657.5 mg, t=202.5 h, and T_half=29.5 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 = 6.21 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 111.8732, "unit": "g"}

Answer: 111.8732

Prompt: A sample contains 6.21 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.21 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 2335 mL to 2.335 L.
3. Compute M = 2.365 / 2.335.
Final: {"answer": 1.0128, "unit": "mol/L"}

Answer: 1.0128

Prompt: A solution contains 2.365 mol of solute in 2335 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2335 mL to 2.335 L.
Compute M = 2.365 / 2.335.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 0.1439, "unit": "state_units"}

Answer: 0.1439

Prompt: Use explicit Euler on dy/dt = -0.58 y with y(0)=2.5, step size h=0.75, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.
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(6.7)=25.58 and f(15.4)=72.56.
3. The interval width is 8.7.
Final: {"answer": 426.909, "unit": "area_units"}

Answer: 426.909

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5.4x+-10.6 from x=6.7 to x=15.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.7)=25.58 and f(15.4)=72.56.
The interval width is 8.7.


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=0.06 and add it to the current value.
Final: {"answer": [1.65, 2.508, 0.682], "unit": "temperature_units"}

Answer: 1.65

Answer: 2.508

Answer: 0.682

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=-1.6, right=2.8; current interior values are [1.8, 2.7, 0.4]. 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 18648.0 / 1000.
Final: {"answer": 18.648, "unit": "kg"}

Answer: 18.648

Prompt: Convert 18648 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 18648.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=275 degrees and keep the unit as newtons.
Final: {"answer": [17.7362, -202.7256], "unit": "N"}

Answer: 17.7362

Answer: -202.7256

Prompt: A vector has magnitude 203.5 N at 275 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=275 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": [0.8, -22.0], "unit": "dimensionless"}

Answer: 0.8

Answer: -22.0

Prompt: A line passes through points (6, -17.2) and (9, -14.8). 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 simulation spec case 81840, 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. Use Newton's second law F = m a.
2. Substitute m = 12.65 kg and a = 4.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 53.7625, "unit": "N"}

Answer: 53.7625

Prompt: A cart has mass 12.65 kg and measured acceleration 4.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 12.65 kg and a = 4.25 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 = 22.65^2 and multiply by 0.5 * 17.65.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 4527.4236, "unit": "J"}

Answer: 4527.4236

Prompt: A body of mass 17.65 kg moves at 22.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 22.65^2 and multiply by 0.5 * 17.65.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=38 degrees through the sine of 2 theta.
3. Substitute v=61.5 m/s and g=9.81 m/s^2.
Final: {"answer": 374.098, "unit": "m"}

Answer: 374.098

Prompt: A projectile is launched on level ground with no air resistance at speed 61.5 m/s and angle 38 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=38 degrees through the sine of 2 theta.
Substitute v=61.5 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 = 2.37 * 8.314 * 420 / 56.9.
Final: {"answer": 145.4439, "unit": "kPa"}

Answer: 145.4439

Prompt: An ideal gas sample has n=2.37 mol, T=420 K, and V=56.9 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 = 2.37 * 8.314 * 420 / 56.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1495 * 0.56 * 10.
Final: {"answer": 8372.0, "unit": "J"}

Answer: 8372.0

Prompt: A 1495 g sample has specific heat 0.56 J/(g*K). How much heat is needed to raise its temperature by 10 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1495 * 0.56 * 10.


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=44.6 V and R=19.9 ohm.
Final: {"answer": 99.9578, "unit": "W"}

Answer: 99.9578

Prompt: A resistor has resistance 19.9 ohm and voltage 44.6 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=44.6 V and R=19.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=72 mg, t=31 h, and T_half=89.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 56.6324, "unit": "mg"}

Answer: 56.6324

Prompt: A radioactive sample starts with 72 mg. Its half-life is 89.5 hours. How many mg remain after 31 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=72 mg, t=31 h, and T_half=89.5 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 2210 mL to 2.21 L.
3. Compute M = 2.375 / 2.21.
Final: {"answer": 1.0747, "unit": "mol/L"}

Answer: 1.0747

Prompt: A solution contains 2.375 mol of solute in 2210 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2210 mL to 2.21 L.
Compute M = 2.375 / 2.21.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.5)=10.7 and f(18.1)=36.5.
3. The interval width is 8.6.
Final: {"answer": 202.96, "unit": "area_units"}

Answer: 202.96

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3x+-17.8 from x=9.5 to x=18.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.5)=10.7 and f(18.1)=36.5.
The interval width is 8.6.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 98.5 + 273.15.
Final: {"answer": 371.65, "unit": "K"}

Answer: 371.65

Prompt: Convert 98.5 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 98.5 + 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": [8.65, -25.0], "unit": "dimensionless"}

Answer: 8.65

Answer: -25.0

Prompt: A line passes through points (17.5, 126.375) and (23.25, 176.113). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In field worksheet case 436059, 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 safe_mean_004084(values):
    if not values:
        raise ValueError('safe_mean requires at least one value')
    return sum(values) / len(values)
```
Final: {"answer": "python_code", "function": "safe_mean_004084"}

Answer: python_code

Prompt: Write a Python function safe_mean_004084(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.

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

try:
    safe_mean_004084([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 17.4 kg and a = 0.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 10.44, "unit": "N"}

Answer: 10.44

Prompt: A cart has mass 17.4 kg and measured acceleration 0.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 17.4 kg and a = 0.6 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=81 degrees through the sine of 2 theta.
3. Substitute v=19.2 m/s and g=9.81 m/s^2.
Final: {"answer": 11.6122, "unit": "m"}

Answer: 11.6122

Prompt: A projectile is launched on level ground with no air resistance at speed 19.2 m/s and angle 81 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=81 degrees through the sine of 2 theta.
Substitute v=19.2 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.18 * 8.314 * 607 / 60.8.
Final: {"answer": 263.9504, "unit": "kPa"}

Answer: 263.9504

Prompt: An ideal gas sample has n=3.18 mol, T=607 K, and V=60.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.18 * 8.314 * 607 / 60.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1855 * 2.965 * 37.
Final: {"answer": 203502.775, "unit": "J"}

Answer: 203502.775

Prompt: A 1855 g sample has specific heat 2.965 J/(g*K). How much heat is needed to raise its temperature by 37 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1855 * 2.965 * 37.


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=168.8 V and R=103.7 ohm.
Final: {"answer": 274.768, "unit": "W"}

Answer: 274.768

Prompt: A resistor has resistance 103.7 ohm and voltage 168.8 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=168.8 V and R=103.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=879.5 mg, t=78 h, and T_half=81.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 453.0368, "unit": "mg"}

Answer: 453.0368

Prompt: A radioactive sample starts with 879.5 mg. Its half-life is 81.5 hours. How many mg remain after 78 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=879.5 mg, t=78 h, and T_half=81.5 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 = 6.91 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 304.1091, "unit": "g"}

Answer: 304.1091

Prompt: A sample contains 6.91 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 = 6.91 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.28 y, so each step multiplies y by 1 - h*0.28.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 2.3531, "unit": "state_units"}

Answer: 2.3531

Prompt: Use explicit Euler on dy/dt = -0.28 y with y(0)=54, step size h=1.05, 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) = -0.28 y, so each step multiplies y by 1 - h*0.28.
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(-9.2)=-63.96 and f(-6.3)=-47.14.
3. The interval width is 2.9.
Final: {"answer": -161.095, "unit": "area_units"}

Answer: -161.095

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5.8x+-10.6 from x=-9.2 to x=-6.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.2)=-63.96 and f(-6.3)=-47.14.
The interval width is 2.9.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -24.5 + 273.15.
Final: {"answer": 248.65, "unit": "K"}

Answer: 248.65

Prompt: Convert -24.5 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 -24.5 + 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": [8.4, -22.25], "unit": "dimensionless"}

Answer: 8.4

Answer: -22.25

Prompt: A line passes through points (-15.5, -152.45) and (-8.75, -95.75). 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. lever arm times force has torque dimensions
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In student derivation case 346220, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def weighted_sum_004102(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_004102"}

Answer: python_code

Prompt: Write a Python function weighted_sum_004102(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_004102([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: target_schema, valid_examples.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each registry experiment record from batch 286702 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use 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 = 1.71 * 8.314 * 253 / 1.6.
Final: {"answer": 2248.0536, "unit": "kPa"}

Answer: 2248.0536

Prompt: An ideal gas sample has n=1.71 mol, T=253 K, and V=1.6 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 = 1.71 * 8.314 * 253 / 1.6.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=50.3 V and R=151 ohm.
Final: {"answer": 16.7556, "unit": "W"}

Answer: 16.7556

Prompt: A resistor has resistance 151 ohm and voltage 50.3 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=50.3 V and R=151 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=164 mg, t=319.5 h, and T_half=31 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.1295, "unit": "mg"}

Answer: 0.1295

Prompt: A radioactive sample starts with 164 mg. Its half-life is 31 hours. How many mg remain after 319.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=164 mg, t=319.5 h, and T_half=31 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 4105 mL to 4.105 L.
3. Compute M = 4.995 / 4.105.
Final: {"answer": 1.2168, "unit": "mol/L"}

Answer: 1.2168

Prompt: A solution contains 4.995 mol of solute in 4105 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4105 mL to 4.105 L.
Compute M = 4.995 / 4.105.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.18 y, so each step multiplies y by 1 - h*0.18.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 3.322, "unit": "state_units"}

Answer: 3.322

Prompt: Use explicit Euler on dy/dt = -0.18 y with y(0)=68.5, step size h=1.95, for 7 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.18 y, so each step multiplies y by 1 - h*0.18.
Apply that update for 7 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-8.2)=4.08 and f(-7.2)=3.68.
3. The interval width is 1.
Final: {"answer": 3.88, "unit": "area_units"}

Answer: 3.88

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.4x+0.8 from x=-8.2 to x=-7.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-8.2)=4.08 and f(-7.2)=3.68.
The interval width is 1.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=235 degrees and keep the unit as newtons.
Final: {"answer": [-138.5187, -197.8252], "unit": "N"}

Answer: -138.5187

Answer: -197.8252

Prompt: A vector has magnitude 241.5 N at 235 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=235 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [5.95, 17.0], "unit": "dimensionless"}

Answer: 5.95

Answer: 17.0

Prompt: A line passes through points (-9.5, -39.525) and (1.75, 27.4125). 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 900786, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def weighted_sum_004120(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_004120"}

Answer: python_code

Prompt: Write a Python function weighted_sum_004120(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_004120([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: left_boundary, right_boundary.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.08 and interior values [1.15, -1.55, -0.55], 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 = 18.85 kg and a = 15.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 298.7725, "unit": "N"}

Answer: 298.7725

Prompt: A cart has mass 18.85 kg and measured acceleration 15.85 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 = 18.85 kg and a = 15.85 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 = 7.8^2 and multiply by 0.5 * 19.65.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 597.753, "unit": "J"}

Answer: 597.753

Prompt: A body of mass 19.65 kg moves at 7.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 7.8^2 and multiply by 0.5 * 19.65.
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 = 2.89 * 8.314 * 281 / 7.4.
Final: {"answer": 912.3941, "unit": "kPa"}

Answer: 912.3941

Prompt: An ideal gas sample has n=2.89 mol, T=281 K, and V=7.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.89 * 8.314 * 281 / 7.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1850 * 2.67 * 35.
Final: {"answer": 172882.5, "unit": "J"}

Answer: 172882.5

Prompt: A 1850 g sample has specific heat 2.67 J/(g*K). How much heat is needed to raise its temperature by 35 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1850 * 2.67 * 35.


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=104.7 V and R=61.8 ohm.
Final: {"answer": 177.3801, "unit": "W"}

Answer: 177.3801

Prompt: A resistor has resistance 61.8 ohm and voltage 104.7 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=104.7 V and R=61.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=504.5 mg, t=86.5 h, and T_half=60 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 185.7275, "unit": "mg"}

Answer: 185.7275

Prompt: A radioactive sample starts with 504.5 mg. Its half-life is 60 hours. How many mg remain after 86.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=504.5 mg, t=86.5 h, and T_half=60 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.66 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 466.4054, "unit": "g"}

Answer: 466.4054

Prompt: A sample contains 4.66 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 = 4.66 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 3335 mL to 3.335 L.
3. Compute M = 1.925 / 3.335.
Final: {"answer": 0.5772, "unit": "mol/L"}

Answer: 0.5772

Prompt: A solution contains 1.925 mol of solute in 3335 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3335 mL to 3.335 L.
Compute M = 1.925 / 3.335.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.
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 = -0.71 y with y(0)=28, step size h=1.25, 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) = -0.71 y, so each step multiplies y by 1 - h*0.71.
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(6.1)=-35.5 and f(8.4)=-49.3.
3. The interval width is 2.3.
Final: {"answer": -97.52, "unit": "area_units"}

Answer: -97.52

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6x+1.1 from x=6.1 to x=8.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.1)=-35.5 and f(8.4)=-49.3.
The interval width is 2.3.


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=0.34 and add it to the current value.
Final: {"answer": [0.18, -0.549, -1.297], "unit": "temperature_units"}

Answer: 0.18

Answer: -0.549

Answer: -1.297

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=-1.8; current interior values are [0.35, -1.45, -0.6]. 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. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=352 degrees and keep the unit as newtons.
Final: {"answer": [382.2435, -53.7208], "unit": "N"}

Answer: 382.2435

Answer: -53.7208

Prompt: A vector has magnitude 386 N at 352 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=352 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": [7.35, 5.5], "unit": "dimensionless"}

Answer: 7.35

Answer: 5.5

Prompt: A line passes through points (-5.75, -36.7625) and (-1.75, -7.3625). Return [slope, intercept] for y = slope*x + intercept.

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


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

```python
def running_total_004138(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_004138"}

Answer: python_code

Prompt: Write a Python function running_total_004138(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=0.73 mol and T=319 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 = 12.55 kg and a = 9.15 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 114.8325, "unit": "N"}

Answer: 114.8325

Prompt: A cart has mass 12.55 kg and measured acceleration 9.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 12.55 kg and a = 9.15 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 11.15^2 and multiply by 0.5 * 24.25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1507.4103, "unit": "J"}

Answer: 1507.4103

Prompt: A body of mass 24.25 kg moves at 11.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 11.15^2 and multiply by 0.5 * 24.25.
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=25 degrees through the sine of 2 theta.
3. Substitute v=14.7 m/s and g=9.81 m/s^2.
Final: {"answer": 16.8741, "unit": "m"}

Answer: 16.8741

Prompt: A projectile is launched on level ground with no air resistance at speed 14.7 m/s and angle 25 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=25 degrees through the sine of 2 theta.
Substitute v=14.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.49 * 8.314 * 476 / 102.7.
Final: {"answer": 18.8818, "unit": "kPa"}

Answer: 18.8818

Prompt: An ideal gas sample has n=0.49 mol, T=476 K, and V=102.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.49 * 8.314 * 476 / 102.7.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 410 * 3.635 * 105.
Final: {"answer": 156486.75, "unit": "J"}

Answer: 156486.75

Prompt: A 410 g sample has specific heat 3.635 J/(g*K). How much heat is needed to raise its temperature by 105 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 410 * 3.635 * 105.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=112.7 V and R=193.7 ohm.
Final: {"answer": 65.572, "unit": "W"}

Answer: 65.572

Prompt: A resistor has resistance 193.7 ohm and voltage 112.7 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=112.7 V and R=193.7 ohm.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(5.4)=27.48 and f(8.5)=48.25.
3. The interval width is 3.1.
Final: {"answer": 117.3815, "unit": "area_units"}

Answer: 117.3815

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.7x+-8.7 from x=5.4 to x=8.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(5.4)=27.48 and f(8.5)=48.25.
The interval width is 3.1.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.44 and add it to the current value.
Final: {"answer": [0.55, 0.194, 0.25], "unit": "temperature_units"}

Answer: 0.55

Answer: 0.194

Answer: 0.25

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=0.4, right=-0.05; current interior values are [0.55, 0.7, -0.3]. Use r=0.44. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.44 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 21501.0 / 1000.
Final: {"answer": 21.501, "unit": "kg"}

Answer: 21.501

Prompt: Convert 21501 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 21501.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=109 degrees and keep the unit as newtons.
Final: {"answer": [-38.7426, 112.5167], "unit": "N"}

Answer: -38.7426

Answer: 112.5167

Prompt: A vector has magnitude 119 N at 109 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=109 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [5.6, -2.75], "unit": "dimensionless"}

Answer: 5.6

Answer: -2.75

Prompt: A line passes through points (12.25, 65.85) and (18.75, 102.25). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. 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 simulation spec case 659591, 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 safe_mean_004156(values):
    if not values:
        raise ValueError('safe_mean requires at least one value')
    return sum(values) / len(values)
```
Final: {"answer": "python_code", "function": "safe_mean_004156"}

Answer: python_code

Prompt: Write a Python function safe_mean_004156(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.

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

try:
    safe_mean_004156([])
    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)=59.5 and h=1, 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 = 19.85 kg and a = 5.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 114.1375, "unit": "N"}

Answer: 114.1375

Prompt: A cart has mass 19.85 kg and measured acceleration 5.75 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 = 19.85 kg and a = 5.75 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 = 28.25^2 and multiply by 0.5 * 0.9.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 359.1281, "unit": "J"}

Answer: 359.1281

Prompt: A body of mass 0.9 kg moves at 28.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 28.25^2 and multiply by 0.5 * 0.9.
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=37 degrees through the sine of 2 theta.
3. Substitute v=45.5 m/s and g=9.81 m/s^2.
Final: {"answer": 202.8595, "unit": "m"}

Answer: 202.8595

Prompt: A projectile is launched on level ground with no air resistance at speed 45.5 m/s and angle 37 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=37 degrees through the sine of 2 theta.
Substitute v=45.5 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 = 2.98 * 8.314 * 345 / 100.4.
Final: {"answer": 85.1357, "unit": "kPa"}

Answer: 85.1357

Prompt: An ideal gas sample has n=2.98 mol, T=345 K, and V=100.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.98 * 8.314 * 345 / 100.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 230 * 3.73 * 11.
Final: {"answer": 9436.9, "unit": "J"}

Answer: 9436.9

Prompt: A 230 g sample has specific heat 3.73 J/(g*K). How much heat is needed to raise its temperature by 11 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 230 * 3.73 * 11.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=864 mg, t=266 h, and T_half=43.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 12.4662, "unit": "mg"}

Answer: 12.4662

Prompt: A radioactive sample starts with 864 mg. Its half-life is 43.5 hours. How many mg remain after 266 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=864 mg, t=266 h, and T_half=43.5 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 = 3.25 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 325.2828, "unit": "g"}

Answer: 325.2828

Prompt: A sample contains 3.25 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 = 3.25 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 4970 mL to 4.97 L.
3. Compute M = 2.135 / 4.97.
Final: {"answer": 0.4296, "unit": "mol/L"}

Answer: 0.4296

Prompt: A solution contains 2.135 mol of solute in 4970 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4970 mL to 4.97 L.
Compute M = 2.135 / 4.97.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-2.7)=1.7 and f(3.7)=-49.5.
3. The interval width is 6.4.
Final: {"answer": -152.96, "unit": "area_units"}

Answer: -152.96

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-8x+-19.9 from x=-2.7 to x=3.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-2.7)=1.7 and f(3.7)=-49.5.
The interval width is 6.4.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.06 and add it to the current value.
Final: {"answer": [0.115, 1.406, 2.509], "unit": "temperature_units"}

Answer: 0.115

Answer: 1.406

Answer: 2.509

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.95, right=-0.65; current interior values are [0.1, 1.4, 2.8]. 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 151.5 + 273.15.
Final: {"answer": 424.65, "unit": "K"}

Answer: 424.65

Prompt: Convert 151.5 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 151.5 + 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=341 degrees and keep the unit as newtons.
Final: {"answer": [253.8717, -87.415], "unit": "N"}

Answer: 253.8717

Answer: -87.415

Prompt: A vector has magnitude 268.5 N at 341 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=341 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": [-9.55, -25.75], "unit": "dimensionless"}

Answer: -9.55

Answer: -25.75

Prompt: A line passes through points (-8.75, 57.8125) and (4.5, -68.725). 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. volt squared divided by ohm is watt
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In field worksheet case 897298, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
volt squared divided by ohm is watt
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: target_schema, valid_examples.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each registry survey record from batch 728508 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 20.55 kg and a = 11.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 236.325, "unit": "N"}

Answer: 236.325

Prompt: A cart has mass 20.55 kg and measured acceleration 11.5 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 = 20.55 kg and a = 11.5 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 = 12.55^2 and multiply by 0.5 * 17.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1338.7713, "unit": "J"}

Answer: 1338.7713

Prompt: A body of mass 17 kg moves at 12.55 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 12.55^2 and multiply by 0.5 * 17.
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=73 degrees through the sine of 2 theta.
3. Substitute v=66.3 m/s and g=9.81 m/s^2.
Final: {"answer": 250.5646, "unit": "m"}

Answer: 250.5646

Prompt: A projectile is launched on level ground with no air resistance at speed 66.3 m/s and angle 73 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=73 degrees through the sine of 2 theta.
Substitute v=66.3 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.26 * 8.314 * 366 / 85.1.
Final: {"answer": 45.0539, "unit": "kPa"}

Answer: 45.0539

Prompt: An ideal gas sample has n=1.26 mol, T=366 K, and V=85.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.26 * 8.314 * 366 / 85.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1590 * 1.955 * 21.
Final: {"answer": 65277.45, "unit": "J"}

Answer: 65277.45

Prompt: A 1590 g sample has specific heat 1.955 J/(g*K). How much heat is needed to raise its temperature by 21 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1590 * 1.955 * 21.


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=137.4 V and R=83.9 ohm.
Final: {"answer": 225.015, "unit": "W"}

Answer: 225.015

Prompt: A resistor has resistance 83.9 ohm and voltage 137.4 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=137.4 V and R=83.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=322.5 mg, t=61.5 h, and T_half=115 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 222.6097, "unit": "mg"}

Answer: 222.6097

Prompt: A radioactive sample starts with 322.5 mg. Its half-life is 115 hours. How many mg remain after 61.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=322.5 mg, t=61.5 h, and T_half=115 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 = 5.44 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 980.0486, "unit": "g"}

Answer: 980.0486

Prompt: A sample contains 5.44 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 = 5.44 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 2075 mL to 2.075 L.
3. Compute M = 0.345 / 2.075.
Final: {"answer": 0.1663, "unit": "mol/L"}

Answer: 0.1663

Prompt: A solution contains 0.345 mol of solute in 2075 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2075 mL to 2.075 L.
Compute M = 0.345 / 2.075.


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": [-0.026, -0.321, 0.674], "unit": "temperature_units"}

Answer: -0.026

Answer: -0.321

Answer: 0.674

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.1, right=2.7; current interior values are [-0.4, -1.8, 1.15]. Use r=0.34. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4021.5 / 100.
Final: {"answer": 40.215, "unit": "m"}

Answer: 40.215

Prompt: Convert 4021.5 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 4021.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=287 degrees and keep the unit as newtons.
Final: {"answer": [89.9043, -294.0637], "unit": "N"}

Answer: 89.9043

Answer: -294.0637

Prompt: A vector has magnitude 307.5 N at 287 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=287 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-2.65, -9.5], "unit": "dimensionless"}

Answer: -2.65

Answer: -9.5

Prompt: A line passes through points (-5.75, 5.7375) and (2.75, -16.7875). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In student derivation case 295054, 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 threshold_flags_004192(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_004192"}

Answer: python_code

Prompt: Write a Python function threshold_flags_004192(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.

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

assert threshold_flags_004192([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_004192([], 5) == []

assert threshold_flags_004192([-1, 0], 0) == [False, True]


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

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each mobile ledger record from batch 593043 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 0.5 kg and a = 2.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 1.275, "unit": "N"}

Answer: 1.275

Prompt: A cart has mass 0.5 kg and measured acceleration 2.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 0.5 kg and a = 2.55 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 28.05^2 and multiply by 0.5 * 3.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1298.2241, "unit": "J"}

Answer: 1298.2241

Prompt: A body of mass 3.3 kg moves at 28.05 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 28.05^2 and multiply by 0.5 * 3.3.
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=58 degrees through the sine of 2 theta.
3. Substitute v=64.6 m/s and g=9.81 m/s^2.
Final: {"answer": 382.3457, "unit": "m"}

Answer: 382.3457

Prompt: A projectile is launched on level ground with no air resistance at speed 64.6 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=64.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.92 * 8.314 * 459 / 22.2.
Final: {"answer": 330.0433, "unit": "kPa"}

Answer: 330.0433

Prompt: An ideal gas sample has n=1.92 mol, T=459 K, and V=22.2 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 = 1.92 * 8.314 * 459 / 22.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 465 * 0.89 * 98.
Final: {"answer": 40557.3, "unit": "J"}

Answer: 40557.3

Prompt: A 465 g sample has specific heat 0.89 J/(g*K). How much heat is needed to raise its temperature by 98 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 465 * 0.89 * 98.


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=150.8 V and R=150.4 ohm.
Final: {"answer": 151.2011, "unit": "W"}

Answer: 151.2011

Prompt: A resistor has resistance 150.4 ohm and voltage 150.8 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=150.8 V and R=150.4 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.73 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1212.4499, "unit": "g"}

Answer: 1212.4499

Prompt: A sample contains 6.73 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 = 6.73 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 1000 mL to 1 L.
3. Compute M = 3.57 / 1.
Final: {"answer": 3.57, "unit": "mol/L"}

Answer: 3.57

Prompt: A solution contains 3.57 mol of solute in 1000 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1000 mL to 1 L.
Compute M = 3.57 / 1.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 2.6228, "unit": "state_units"}

Answer: 2.6228

Prompt: Use explicit Euler on dy/dt = -0.08 y with y(0)=9, step size h=1.45, for 10 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.
Apply that update for 10 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=0.36 and add it to the current value.
Final: {"answer": [1.312, 1.462, -0.254], "unit": "temperature_units"}

Answer: 1.312

Answer: 1.462

Answer: -0.254

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.4, right=-1.55; current interior values are [2.95, -0.05, 1.15]. 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. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-1.5, 8.25], "unit": "dimensionless"}

Answer: -1.5

Answer: 8.25

Prompt: A line passes through points (17.25, -17.625) and (19.25, -20.625). Return [slope, intercept] for y = slope*x + intercept.

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


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

```python
def clamp_004210(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_004210"}

Answer: python_code

Prompt: Write a Python function clamp_004210(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.

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

try:
    clamp_004210(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid mobile invoice records in release 338249, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 21.35^2 and multiply by 0.5 * 27.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 6221.9771, "unit": "J"}

Answer: 6221.9771

Prompt: A body of mass 27.3 kg moves at 21.35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 21.35^2 and multiply by 0.5 * 27.3.
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=37 degrees through the sine of 2 theta.
3. Substitute v=20.5 m/s and g=9.81 m/s^2.
Final: {"answer": 41.1794, "unit": "m"}

Answer: 41.1794

Prompt: A projectile is launched on level ground with no air resistance at speed 20.5 m/s and angle 37 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=37 degrees through the sine of 2 theta.
Substitute v=20.5 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 = 545 * 0.665 * 2.
Final: {"answer": 724.85, "unit": "J"}

Answer: 724.85

Prompt: A 545 g sample has specific heat 0.665 J/(g*K). How much heat is needed to raise its temperature by 2 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 545 * 0.665 * 2.


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=175.1 V and R=169.6 ohm.
Final: {"answer": 180.7784, "unit": "W"}

Answer: 180.7784

Prompt: A resistor has resistance 169.6 ohm and voltage 175.1 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=175.1 V and R=169.6 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=293.5 mg, t=268.5 h, and T_half=24 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.1258, "unit": "mg"}

Answer: 0.1258

Prompt: A radioactive sample starts with 293.5 mg. Its half-life is 24 hours. How many mg remain after 268.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=293.5 mg, t=268.5 h, and T_half=24 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.15 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 125.646, "unit": "g"}

Answer: 125.646

Prompt: A sample contains 2.15 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 = 2.15 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 1670 mL to 1.67 L.
3. Compute M = 0.015 / 1.67.
Final: {"answer": 0.009, "unit": "mol/L"}

Answer: 0.009

Prompt: A solution contains 0.015 mol of solute in 1670 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1670 mL to 1.67 L.
Compute M = 0.015 / 1.67.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 12.2351, "unit": "state_units"}

Answer: 12.2351

Prompt: Use explicit Euler on dy/dt = -0.88 y with y(0)=73.5, step size h=1.6, for 2 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.
Apply that update for 2 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-7.5)=63.4 and f(-5.7)=51.52.
3. The interval width is 1.8.
Final: {"answer": 103.428, "unit": "area_units"}

Answer: 103.428

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.6x+13.9 from x=-7.5 to x=-5.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.5)=63.4 and f(-5.7)=51.52.
The interval width is 1.8.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.08 and add it to the current value.
Final: {"answer": [0.58, 0.548, 2.72], "unit": "temperature_units"}

Answer: 0.58

Answer: 0.548

Answer: 2.72

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=-0.4, right=2.2; current interior values are [0.7, 0.3, 3.0]. Use r=0.08. 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=0.08 and add it to the current value.