Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.42 and add it to the current value.
Final: {"answer": [-1.122, 0.725, 0.338], "unit": "temperature_units"}

Answer: -1.122

Answer: 0.725

Answer: 0.338

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.4, right=2.4; current interior values are [1.65, -1.9, 0.8]. Use r=0.42. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 5.5 + 273.15.
Final: {"answer": 278.65, "unit": "K"}

Answer: 278.65

Prompt: Convert 5.5 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 5.5 + 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=107 degrees and keep the unit as newtons.
Final: {"answer": [-50.2879, 164.4844], "unit": "N"}

Answer: -50.2879

Answer: 164.4844

Prompt: A vector has magnitude 172 N at 107 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=107 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": [9.8, -28.25], "unit": "dimensionless"}

Answer: 9.8

Answer: -28.25

Prompt: A line passes through points (-10.25, -128.7) and (-6.5, -91.95). Return [slope, intercept] for y = slope*x + intercept.

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


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

```python
def center_values_004660(values):
    if not values:
        raise ValueError('center_values requires at least one value')
    mean = sum(values) / len(values)
    return [value - mean for value in values]
```
Final: {"answer": "python_code", "function": "center_values_004660"}

Answer: python_code

Prompt: Write a Python function center_values_004660(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.

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

try:
    center_values_004660([])
    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=0.46 and interior values [-0.15, 0.2, 0.05], 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 = 7.15 kg and a = 12.4 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 88.66, "unit": "N"}

Answer: 88.66

Prompt: A cart has mass 7.15 kg and measured acceleration 12.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 7.15 kg and a = 12.4 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 22.1^2 and multiply by 0.5 * 5.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1233.2353, "unit": "J"}

Answer: 1233.2353

Prompt: A body of mass 5.05 kg moves at 22.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 22.1^2 and multiply by 0.5 * 5.05.
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 = 4.61 * 8.314 * 406 / 62.9.
Final: {"answer": 247.3924, "unit": "kPa"}

Answer: 247.3924

Prompt: An ideal gas sample has n=4.61 mol, T=406 K, and V=62.9 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 = 4.61 * 8.314 * 406 / 62.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1105 * 4.81 * 67.
Final: {"answer": 356108.35, "unit": "J"}

Answer: 356108.35

Prompt: A 1105 g sample has specific heat 4.81 J/(g*K). How much heat is needed to raise its temperature by 67 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1105 * 4.81 * 67.


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=68.9 V and R=81.4 ohm.
Final: {"answer": 58.3195, "unit": "W"}

Answer: 58.3195

Prompt: A resistor has resistance 81.4 ohm and voltage 68.9 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=68.9 V and R=81.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=284 mg, t=249.5 h, and T_half=100 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 50.3789, "unit": "mg"}

Answer: 50.3789

Prompt: A radioactive sample starts with 284 mg. Its half-life is 100 hours. How many mg remain after 249.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=284 mg, t=249.5 h, and T_half=100 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 = 1.95 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 195.1696, "unit": "g"}

Answer: 195.1696

Prompt: A sample contains 1.95 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 = 1.95 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 60 mL to 0.06 L.
3. Compute M = 3.175 / 0.06.
Final: {"answer": 52.9167, "unit": "mol/L"}

Answer: 52.9167

Prompt: A solution contains 3.175 mol of solute in 60 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 60 mL to 0.06 L.
Compute M = 3.175 / 0.06.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.5 y, so each step multiplies y by 1 - h*0.5.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 16.3223, "unit": "state_units"}

Answer: 16.3223

Prompt: Use explicit Euler on dy/dt = -0.5 y with y(0)=19, step size h=0.05, for 6 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.5 y, so each step multiplies y by 1 - h*0.5.
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=0.02 and add it to the current value.
Final: {"answer": [-1.212, 0.575, -1.103], "unit": "temperature_units"}

Answer: -1.212

Answer: 0.575

Answer: -1.103

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=-1.25, right=1.8; current interior values are [-1.25, 0.65, -1.2]. Use r=0.02. 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=0.02 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=248 degrees and keep the unit as newtons.
Final: {"answer": [-187.3033, -463.5919], "unit": "N"}

Answer: -187.3033

Answer: -463.5919

Prompt: A vector has magnitude 500 N at 248 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=248 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": [1.25, -28.25], "unit": "dimensionless"}

Answer: 1.25

Answer: -28.25

Prompt: A line passes through points (13.25, -11.6875) and (14, -10.75). 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. speed squared over acceleration has units of meters
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In sensor calibration case 548733, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
speed squared over acceleration has units of meters
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_004678(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_004678"}

Answer: python_code

Prompt: Write a Python function threshold_flags_004678(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_004678([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_004678([], 5) == []

assert threshold_flags_004678([-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: required_fields, allowed_transformations.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid billing sensor records in release 425325, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 4.85 kg and a = 7.05 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 34.1925, "unit": "N"}

Answer: 34.1925

Prompt: A cart has mass 4.85 kg and measured acceleration 7.05 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 = 4.85 kg and a = 7.05 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 = 40.2^2 and multiply by 0.5 * 11.55.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 9332.631, "unit": "J"}

Answer: 9332.631

Prompt: A body of mass 11.55 kg moves at 40.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 40.2^2 and multiply by 0.5 * 11.55.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=27 degrees through the sine of 2 theta.
3. Substitute v=70.4 m/s and g=9.81 m/s^2.
Final: {"answer": 408.7276, "unit": "m"}

Answer: 408.7276

Prompt: A projectile is launched on level ground with no air resistance at speed 70.4 m/s and angle 27 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=27 degrees through the sine of 2 theta.
Substitute v=70.4 m/s and g=9.81 m/s^2.

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


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.58 * 8.314 * 467 / 57.6.
Final: {"answer": 106.5029, "unit": "kPa"}

Answer: 106.5029

Prompt: An ideal gas sample has n=1.58 mol, T=467 K, and V=57.6 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 = 1.58 * 8.314 * 467 / 57.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1885 * 4.26 * 21.
Final: {"answer": 168632.1, "unit": "J"}

Answer: 168632.1

Prompt: A 1885 g sample has specific heat 4.26 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 = 1885 * 4.26 * 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=129.9 V and R=125.9 ohm.
Final: {"answer": 134.0271, "unit": "W"}

Answer: 134.0271

Prompt: A resistor has resistance 125.9 ohm and voltage 129.9 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=129.9 V and R=125.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=540.5 mg, t=189.5 h, and T_half=35.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 13.3625, "unit": "mg"}

Answer: 13.3625

Prompt: A radioactive sample starts with 540.5 mg. Its half-life is 35.5 hours. How many mg remain after 189.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=540.5 mg, t=189.5 h, and T_half=35.5 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 = 1.17 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 51.4917, "unit": "g"}

Answer: 51.4917

Prompt: A sample contains 1.17 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 = 1.17 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) = -0.85 y, so each step multiplies y by 1 - h*0.85.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 0.0219, "unit": "state_units"}

Answer: 0.0219

Prompt: Use explicit Euler on dy/dt = -0.85 y with y(0)=73.5, step size h=0.75, for 8 steps. What is y after the final step?

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


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.38 and add it to the current value.
Final: {"answer": [0.388, 0.0, -0.746], "unit": "temperature_units"}

Answer: 0.388

Answer: 0.0

Answer: -0.746

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=1.5, right=0.6; current interior values are [2.25, -1.9, -1.05]. Use r=0.38. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 564.0 / 100.
Final: {"answer": 5.64, "unit": "m"}

Answer: 5.64

Prompt: Convert 564 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 564.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=222 degrees and keep the unit as newtons.
Final: {"answer": [-202.1354, -182.0035], "unit": "N"}

Answer: -202.1354

Answer: -182.0035

Prompt: A vector has magnitude 272 N at 222 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=222 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. velocity times time gives distance, not acceleration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In quality-control check case 179575, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
velocity times time gives distance, not acceleration
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


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

```python
def weighted_sum_004696(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_004696"}

Answer: python_code

Prompt: Write a Python function weighted_sum_004696(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_004696([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 13.4 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 17.65 kg and a = 15.15 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 267.3975, "unit": "N"}

Answer: 267.3975

Prompt: A cart has mass 17.65 kg and measured acceleration 15.15 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 = 17.65 kg and a = 15.15 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 = 16.7^2 and multiply by 0.5 * 15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2091.675, "unit": "J"}

Answer: 2091.675

Prompt: A body of mass 15 kg moves at 16.7 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 16.7^2 and multiply by 0.5 * 15.
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=69.5 m/s and g=9.81 m/s^2.
Final: {"answer": 477.7544, "unit": "m"}

Answer: 477.7544

Prompt: A projectile is launched on level ground with no air resistance at speed 69.5 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=69.5 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 = 1600 * 2.4 * 113.
Final: {"answer": 433920.0, "unit": "J"}

Answer: 433920.0

Prompt: A 1600 g sample has specific heat 2.4 J/(g*K). How much heat is needed to raise its temperature by 113 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1600 * 2.4 * 113.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=983.5 mg, t=136 h, and T_half=9.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0482, "unit": "mg"}

Answer: 0.0482

Prompt: A radioactive sample starts with 983.5 mg. Its half-life is 9.5 hours. How many mg remain after 136 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=983.5 mg, t=136 h, and T_half=9.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.87 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 459.9228, "unit": "g"}

Answer: 459.9228

Prompt: A sample contains 7.87 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.87 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.45 y, so each step multiplies y by 1 - h*0.45.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 0.5245, "unit": "state_units"}

Answer: 0.5245

Prompt: Use explicit Euler on dy/dt = -0.45 y with y(0)=12.5, step size h=1.45, for 3 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.45 y, so each step multiplies y by 1 - h*0.45.
Apply that update for 3 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(4)=-9.9 and f(9.5)=-32.45.
3. The interval width is 5.5.
Final: {"answer": -116.4625, "unit": "area_units"}

Answer: -116.4625

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.1x+6.5 from x=4 to x=9.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4)=-9.9 and f(9.5)=-32.45.
The interval width is 5.5.

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


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.44 and add it to the current value.
Final: {"answer": [0.28, -1.336, -1.116], "unit": "temperature_units"}

Answer: 0.28

Answer: -1.336

Answer: -1.116

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, right=-1.05; current interior values are [-1.15, -1.05, -1.6]. 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 32689.0 / 1000.
Final: {"answer": 32.689, "unit": "kg"}

Answer: 32.689

Prompt: Convert 32689 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 32689.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=234 degrees and keep the unit as newtons.
Final: {"answer": [-189.5607, -260.908], "unit": "N"}

Answer: -189.5607

Answer: -260.908

Prompt: A vector has magnitude 322.5 N at 234 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=234 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [6.9, 9.5], "unit": "dimensionless"}

Answer: 6.9

Answer: 9.5

Prompt: A line passes through points (2.5, 26.75) and (15, 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. grams cancel with J/(g*K), and kelvin cancels, leaving joules
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In simulation spec case 937225, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def safe_mean_004714(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_004714"}

Answer: python_code

Prompt: Write a Python function safe_mean_004714(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_004714([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 13.7 kg and a = 4.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 61.65, "unit": "N"}

Answer: 61.65

Prompt: A cart has mass 13.7 kg and measured acceleration 4.5 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 = 13.7 kg and a = 4.5 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=7 degrees through the sine of 2 theta.
3. Substitute v=17.3 m/s and g=9.81 m/s^2.
Final: {"answer": 7.3807, "unit": "m"}

Answer: 7.3807

Prompt: A projectile is launched on level ground with no air resistance at speed 17.3 m/s and angle 7 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=7 degrees through the sine of 2 theta.
Substitute v=17.3 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 = 1.34 * 8.314 * 584 / 15.0.
Final: {"answer": 433.7469, "unit": "kPa"}

Answer: 433.7469

Prompt: An ideal gas sample has n=1.34 mol, T=584 K, and V=15.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.34 * 8.314 * 584 / 15.0.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=150.4 V and R=66.3 ohm.
Final: {"answer": 341.1789, "unit": "W"}

Answer: 341.1789

Prompt: A resistor has resistance 66.3 ohm and voltage 150.4 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=150.4 V and R=66.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=681.5 mg, t=185.5 h, and T_half=15.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.1701, "unit": "mg"}

Answer: 0.1701

Prompt: A radioactive sample starts with 681.5 mg. Its half-life is 15.5 hours. How many mg remain after 185.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=681.5 mg, t=185.5 h, and T_half=15.5 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 = 3.44 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 61.9716, "unit": "g"}

Answer: 61.9716

Prompt: A sample contains 3.44 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 3.44 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(1.6)=29.08 and f(8)=69.4.
3. The interval width is 6.4.
Final: {"answer": 315.136, "unit": "area_units"}

Answer: 315.136

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.3x+19 from x=1.6 to x=8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.6)=29.08 and f(8)=69.4.
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=0.42 and add it to the current value.
Final: {"answer": [0.175, -0.523, 0.942], "unit": "temperature_units"}

Answer: 0.175

Answer: -0.523

Answer: 0.942

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.25, right=1.9; current interior values are [-0.35, 0.8, -1.2]. Use r=0.42. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=6 degrees and keep the unit as newtons.
Final: {"answer": [130.7796, 13.7455], "unit": "N"}

Answer: 130.7796

Answer: 13.7455

Prompt: A vector has magnitude 131.5 N at 6 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=6 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": [-5.65, -16.75], "unit": "dimensionless"}

Answer: -5.65

Answer: -16.75

Prompt: A line passes through points (3.25, -35.1125) and (15.75, -105.738). 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. speed squared over acceleration has units of meters
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In lab notebook case 744926, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
speed squared over acceleration has units of meters
The equation is valid only if both sides have identical dimensions.

Answer: consistent


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

```python
def running_total_004732(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_004732"}

Answer: python_code

Prompt: Write a Python function running_total_004732(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: 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)=58.5 and h=1.65, 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 = 16.6 kg and a = 3.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 57.27, "unit": "N"}

Answer: 57.27

Prompt: A cart has mass 16.6 kg and measured acceleration 3.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 16.6 kg and a = 3.45 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 14.35^2 and multiply by 0.5 * 5.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 602.3233, "unit": "J"}

Answer: 602.3233

Prompt: A body of mass 5.85 kg moves at 14.35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 14.35^2 and multiply by 0.5 * 5.85.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=21 degrees through the sine of 2 theta.
3. Substitute v=12.1 m/s and g=9.81 m/s^2.
Final: {"answer": 9.9865, "unit": "m"}

Answer: 9.9865

Prompt: A projectile is launched on level ground with no air resistance at speed 12.1 m/s and angle 21 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=21 degrees through the sine of 2 theta.
Substitute v=12.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.46 * 8.314 * 317 / 89.6.
Final: {"answer": 131.1886, "unit": "kPa"}

Answer: 131.1886

Prompt: An ideal gas sample has n=4.46 mol, T=317 K, and V=89.6 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 = 4.46 * 8.314 * 317 / 89.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1295 * 1.535 * 102.
Final: {"answer": 202758.15, "unit": "J"}

Answer: 202758.15

Prompt: A 1295 g sample has specific heat 1.535 J/(g*K). How much heat is needed to raise its temperature by 102 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1295 * 1.535 * 102.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.86 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 37.8486, "unit": "g"}

Answer: 37.8486

Prompt: A sample contains 0.86 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.86 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2905 mL to 2.905 L.
3. Compute M = 4.74 / 2.905.
Final: {"answer": 1.6317, "unit": "mol/L"}

Answer: 1.6317

Prompt: A solution contains 4.74 mol of solute in 2905 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2905 mL to 2.905 L.
Compute M = 4.74 / 2.905.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 0.0038, "unit": "state_units"}

Answer: 0.0038

Prompt: Use explicit Euler on dy/dt = -0.59 y with y(0)=24, step size h=1.4, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.
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(-3.9)=7.03 and f(3.4)=31.12.
3. The interval width is 7.3.
Final: {"answer": 139.2475, "unit": "area_units"}

Answer: 139.2475

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.3x+19.9 from x=-3.9 to x=3.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-3.9)=7.03 and f(3.4)=31.12.
The interval width is 7.3.


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=0.16 and add it to the current value.
Final: {"answer": [1.304, 1.1, 0.728], "unit": "temperature_units"}

Answer: 1.304

Answer: 1.1

Answer: 0.728

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.45, right=2.6; current interior values are [2.0, 1.1, 0.2]. Use r=0.16. 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=0.16 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 6732.0 / 1000.
Final: {"answer": 6.732, "unit": "kg"}

Answer: 6.732

Prompt: Convert 6732 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 6732.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=55 degrees and keep the unit as newtons.
Final: {"answer": [143.1073, 204.3784], "unit": "N"}

Answer: 143.1073

Answer: 204.3784

Prompt: A vector has magnitude 249.5 N at 55 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=55 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": [7.65, 7.25], "unit": "dimensionless"}

Answer: 7.65

Answer: 7.25

Prompt: A line passes through points (-11.75, -82.6375) and (-3.75, -21.4375). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In lab notebook case 482226, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each mobile invoice record from batch 473955 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 = 7.8 kg and a = 14.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 113.88, "unit": "N"}

Answer: 113.88

Prompt: A cart has mass 7.8 kg and measured acceleration 14.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 7.8 kg and a = 14.6 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 36.45^2 and multiply by 0.5 * 21.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 14083.1865, "unit": "J"}

Answer: 14083.1865

Prompt: A body of mass 21.2 kg moves at 36.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 36.45^2 and multiply by 0.5 * 21.2.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.5 * 8.314 * 320 / 46.7.
Final: {"answer": 199.3936, "unit": "kPa"}

Answer: 199.3936

Prompt: An ideal gas sample has n=3.5 mol, T=320 K, and V=46.7 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 = 3.5 * 8.314 * 320 / 46.7.


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=25.4 V and R=66.4 ohm.
Final: {"answer": 9.7163, "unit": "W"}

Answer: 9.7163

Prompt: A resistor has resistance 66.4 ohm and voltage 25.4 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=25.4 V and R=66.4 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.88 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 51.4272, "unit": "g"}

Answer: 51.4272

Prompt: A sample contains 0.88 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 = 0.88 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(1.3)=5.85 and f(6.3)=-21.65.
3. The interval width is 5.
Final: {"answer": -39.5, "unit": "area_units"}

Answer: -39.5

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.5x+13 from x=1.3 to x=6.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.3)=5.85 and f(6.3)=-21.65.
The interval width is 5.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 54.5 + 273.15.
Final: {"answer": 327.65, "unit": "K"}

Answer: 327.65

Prompt: Convert 54.5 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 54.5 + 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=110 degrees and keep the unit as newtons.
Final: {"answer": [-137.4921, 377.7564], "unit": "N"}

Answer: -137.4921

Answer: 377.7564

Prompt: A vector has magnitude 402 N at 110 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=110 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": [5.65, -19.25], "unit": "dimensionless"}

Answer: 5.65

Answer: -19.25

Prompt: A line passes through points (8.5, 28.775) and (11.25, 44.3125). 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 model card equation case 36008, 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: 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)=78 and h=0.3, 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 = 19.55 kg and a = 6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 117.3, "unit": "N"}

Answer: 117.3

Prompt: A cart has mass 19.55 kg and measured acceleration 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 = 19.55 kg and a = 6 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 7.55^2 and multiply by 0.5 * 25.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 718.2315, "unit": "J"}

Answer: 718.2315

Prompt: A body of mass 25.2 kg moves at 7.55 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 7.55^2 and multiply by 0.5 * 25.2.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=16 degrees through the sine of 2 theta.
3. Substitute v=49.6 m/s and g=9.81 m/s^2.
Final: {"answer": 132.8936, "unit": "m"}

Answer: 132.8936

Prompt: A projectile is launched on level ground with no air resistance at speed 49.6 m/s and angle 16 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=16 degrees through the sine of 2 theta.
Substitute v=49.6 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 = 730 * 3.375 * 109.
Final: {"answer": 268548.75, "unit": "J"}

Answer: 268548.75

Prompt: A 730 g sample has specific heat 3.375 J/(g*K). How much heat is needed to raise its temperature by 109 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 730 * 3.375 * 109.


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=231.6 V and R=186.2 ohm.
Final: {"answer": 288.0696, "unit": "W"}

Answer: 288.0696

Prompt: A resistor has resistance 186.2 ohm and voltage 231.6 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=231.6 V and R=186.2 ohm.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.93 y, so each step multiplies y by 1 - h*0.93.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 0.0122, "unit": "state_units"}

Answer: 0.0122

Prompt: Use explicit Euler on dy/dt = -0.93 y with y(0)=56, step size h=1.45, 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) = -0.93 y, so each step multiplies y by 1 - h*0.93.
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(-2)=6.6 and f(0.9)=8.34.
3. The interval width is 2.9.
Final: {"answer": 21.663, "unit": "area_units"}

Answer: 21.663

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.6x+7.8 from x=-2 to x=0.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-2)=6.6 and f(0.9)=8.34.
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 -19.0 + 273.15.
Final: {"answer": 254.15, "unit": "K"}

Answer: 254.15

Prompt: Convert -19 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 -19.0 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=36 degrees and keep the unit as newtons.
Final: {"answer": [292.8642, 212.7783], "unit": "N"}

Answer: 292.8642

Answer: 212.7783

Prompt: A vector has magnitude 362 N at 36 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=36 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": [-9.95, -17.75], "unit": "dimensionless"}

Answer: -9.95

Answer: -17.75

Prompt: A line passes through points (13.25, -149.587) and (17.5, -191.875). 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 589744, 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: volume.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=4.34 mol and T=423 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 = 9.75 kg and a = 2.7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 26.325, "unit": "N"}

Answer: 26.325

Prompt: A cart has mass 9.75 kg and measured acceleration 2.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 9.75 kg and a = 2.7 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 44.1^2 and multiply by 0.5 * 21.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 20469.1253, "unit": "J"}

Answer: 20469.1253

Prompt: A body of mass 21.05 kg moves at 44.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 44.1^2 and multiply by 0.5 * 21.05.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=17 degrees through the sine of 2 theta.
3. Substitute v=71.6 m/s and g=9.81 m/s^2.
Final: {"answer": 292.2259, "unit": "m"}

Answer: 292.2259

Prompt: A projectile is launched on level ground with no air resistance at speed 71.6 m/s and angle 17 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=17 degrees through the sine of 2 theta.
Substitute v=71.6 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 = 1.08 * 8.314 * 599 / 53.2.
Final: {"answer": 101.0995, "unit": "kPa"}

Answer: 101.0995

Prompt: An ideal gas sample has n=1.08 mol, T=599 K, and V=53.2 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 = 1.08 * 8.314 * 599 / 53.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 275 * 0.61 * 41.
Final: {"answer": 6877.75, "unit": "J"}

Answer: 6877.75

Prompt: A 275 g sample has specific heat 0.61 J/(g*K). How much heat is needed to raise its temperature by 41 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 275 * 0.61 * 41.


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=90.4 V and R=181.4 ohm.
Final: {"answer": 45.0505, "unit": "W"}

Answer: 45.0505

Prompt: A resistor has resistance 181.4 ohm and voltage 90.4 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=90.4 V and R=181.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=78 mg, t=253.5 h, and T_half=32 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.3216, "unit": "mg"}

Answer: 0.3216

Prompt: A radioactive sample starts with 78 mg. Its half-life is 32 hours. How many mg remain after 253.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=78 mg, t=253.5 h, and T_half=32 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 2430 mL to 2.43 L.
3. Compute M = 0.55 / 2.43.
Final: {"answer": 0.2263, "unit": "mol/L"}

Answer: 0.2263

Prompt: A solution contains 0.55 mol of solute in 2430 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2430 mL to 2.43 L.
Compute M = 0.55 / 2.43.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0313, "unit": "state_units"}

Answer: 0.0313

Prompt: Use explicit Euler on dy/dt = -0.42 y with y(0)=10.5, step size h=1.05, 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) = -0.42 y, so each step multiplies y by 1 - h*0.42.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(7.3)=50.44 and f(8.9)=58.12.
3. The interval width is 1.6.
Final: {"answer": 86.848, "unit": "area_units"}

Answer: 86.848

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.8x+15.4 from x=7.3 to x=8.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7.3)=50.44 and f(8.9)=58.12.
The interval width is 1.6.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.44 and add it to the current value.
Final: {"answer": [1.426, 0.06, 1.112], "unit": "temperature_units"}

Answer: 1.426

Answer: 0.06

Answer: 1.112

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=2.05, right=0.6; current interior values are [-1.5, 1.6, 1.2]. Use r=0.44. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4268.0 / 100.
Final: {"answer": 42.68, "unit": "m"}

Answer: 42.68

Prompt: Convert 4268 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 4268.0 / 100.


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": [7.45, 6.75], "unit": "dimensionless"}

Answer: 7.45

Answer: 6.75

Prompt: A line passes through points (-2.25, -10.0125) and (0.5, 10.475). 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. 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)=54 and h=0.6, 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 = 21.05 kg and a = 6.8 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 143.14, "unit": "N"}

Answer: 143.14

Prompt: A cart has mass 21.05 kg and measured acceleration 6.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 21.05 kg and a = 6.8 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=8 degrees through the sine of 2 theta.
3. Substitute v=80.2 m/s and g=9.81 m/s^2.
Final: {"answer": 180.7248, "unit": "m"}

Answer: 180.7248

Prompt: A projectile is launched on level ground with no air resistance at speed 80.2 m/s and angle 8 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=8 degrees through the sine of 2 theta.
Substitute v=80.2 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 = 4.02 * 8.314 * 263 / 89.4.
Final: {"answer": 98.3228, "unit": "kPa"}

Answer: 98.3228

Prompt: An ideal gas sample has n=4.02 mol, T=263 K, and V=89.4 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 = 4.02 * 8.314 * 263 / 89.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 385 * 4.945 * 68.
Final: {"answer": 129460.1, "unit": "J"}

Answer: 129460.1

Prompt: A 385 g sample has specific heat 4.945 J/(g*K). How much heat is needed to raise its temperature by 68 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 385 * 4.945 * 68.


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=121.6 V and R=199.9 ohm.
Final: {"answer": 73.9698, "unit": "W"}

Answer: 73.9698

Prompt: A resistor has resistance 199.9 ohm and voltage 121.6 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=121.6 V and R=199.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=52.5 mg, t=96.5 h, and T_half=66.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 19.2011, "unit": "mg"}

Answer: 19.2011

Prompt: A radioactive sample starts with 52.5 mg. Its half-life is 66.5 hours. How many mg remain after 96.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=52.5 mg, t=96.5 h, and T_half=66.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.66 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 330.7704, "unit": "g"}

Answer: 330.7704

Prompt: A sample contains 5.66 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.66 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3895 mL to 3.895 L.
3. Compute M = 4.015 / 3.895.
Final: {"answer": 1.0308, "unit": "mol/L"}

Answer: 1.0308

Prompt: A solution contains 4.015 mol of solute in 3895 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3895 mL to 3.895 L.
Compute M = 4.015 / 3.895.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 62.1752, "unit": "state_units"}

Answer: 62.1752

Prompt: Use explicit Euler on dy/dt = -0.03 y with y(0)=74.5, step size h=1.95, for 3 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.
Apply that update for 3 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=0.08 and add it to the current value.
Final: {"answer": [1.236, 1.82, 2.534], "unit": "temperature_units"}

Answer: 1.236

Answer: 1.82

Answer: 2.534

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.05, right=2.05; current interior values are [1.2, 1.8, 2.65]. 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.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 744.0 / 1000.
Final: {"answer": 0.744, "unit": "kg"}

Answer: 0.744

Prompt: Convert 744 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 744.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=9 degrees and keep the unit as newtons.
Final: {"answer": [56.7921, 8.995], "unit": "N"}

Answer: 56.7921

Answer: 8.995

Prompt: A vector has magnitude 57.5 N at 9 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=9 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [2.05, 12.0], "unit": "dimensionless"}

Answer: 2.05

Answer: 12.0

Prompt: A line passes through points (-7.25, -2.8625) and (6.25, 24.8125). 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 model card equation case 559878, 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. Use Newton's second law F = m a.
2. Substitute m = 23.85 kg and a = 6.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 155.025, "unit": "N"}

Answer: 155.025

Prompt: A cart has mass 23.85 kg and measured acceleration 6.5 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 = 23.85 kg and a = 6.5 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 = 16.1^2 and multiply by 0.5 * 8.1.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1049.8005, "unit": "J"}

Answer: 1049.8005

Prompt: A body of mass 8.1 kg moves at 16.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 16.1^2 and multiply by 0.5 * 8.1.
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=82 degrees through the sine of 2 theta.
3. Substitute v=7.1 m/s and g=9.81 m/s^2.
Final: {"answer": 1.4164, "unit": "m"}

Answer: 1.4164

Prompt: A projectile is launched on level ground with no air resistance at speed 7.1 m/s and angle 82 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=82 degrees through the sine of 2 theta.
Substitute v=7.1 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 = 1465 * 3.945 * 78.
Final: {"answer": 450795.15, "unit": "J"}

Answer: 450795.15

Prompt: A 1465 g sample has specific heat 3.945 J/(g*K). How much heat is needed to raise its temperature by 78 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1465 * 3.945 * 78.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=203.5 V and R=80.2 ohm.
Final: {"answer": 516.3622, "unit": "W"}

Answer: 516.3622

Prompt: A resistor has resistance 80.2 ohm and voltage 203.5 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=203.5 V and R=80.2 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=826 mg, t=36 h, and T_half=14.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 147.773, "unit": "mg"}

Answer: 147.773

Prompt: A radioactive sample starts with 826 mg. Its half-life is 14.5 hours. How many mg remain after 36 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=826 mg, t=36 h, and T_half=14.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.1 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 414.924, "unit": "g"}

Answer: 414.924

Prompt: A sample contains 7.1 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.1 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 2820 mL to 2.82 L.
3. Compute M = 1.34 / 2.82.
Final: {"answer": 0.4752, "unit": "mol/L"}

Answer: 0.4752

Prompt: A solution contains 1.34 mol of solute in 2820 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2820 mL to 2.82 L.
Compute M = 1.34 / 2.82.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.83 y, so each step multiplies y by 1 - h*0.83.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 1.6647, "unit": "state_units"}

Answer: 1.6647

Prompt: Use explicit Euler on dy/dt = -0.83 y with y(0)=51.5, step size h=0.35, 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) = -0.83 y, so each step multiplies y by 1 - h*0.83.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(8.5)=3.25 and f(18.4)=22.06.
3. The interval width is 9.9.
Final: {"answer": 125.2845, "unit": "area_units"}

Answer: 125.2845

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.9x+-12.9 from x=8.5 to x=18.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(8.5)=3.25 and f(18.4)=22.06.
The interval width is 9.9.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.38 and add it to the current value.
Final: {"answer": [-0.112, -0.25, -0.551], "unit": "temperature_units"}

Answer: -0.112

Answer: -0.25

Answer: -0.551

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.9, right=-1.55; current interior values are [-0.15, 0.7, -0.95]. Use r=0.38. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 49262.0 / 1000.
Final: {"answer": 49.262, "unit": "kg"}

Answer: 49.262

Prompt: Convert 49262 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 49262.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=215 degrees and keep the unit as newtons.
Final: {"answer": [-348.1396, -243.77], "unit": "N"}

Answer: -348.1396

Answer: -243.77

Prompt: A vector has magnitude 425 N at 215 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=215 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": [-0.4, -20.25], "unit": "dimensionless"}

Answer: -0.4

Answer: -20.25

Prompt: A line passes through points (-8.5, -16.85) and (5, -22.25). Return [slope, intercept] for y = slope*x + intercept.

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


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

```python
def finite_differences_004840(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_004840"}

Answer: python_code

Prompt: Write a Python function finite_differences_004840(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.

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

assert finite_differences_004840([5]) == []

assert finite_differences_004840([]) == []


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=4.54 mol and T=504 K, but does not give volume. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 5.55 kg and a = 1.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 8.6025, "unit": "N"}

Answer: 8.6025

Prompt: A cart has mass 5.55 kg and measured acceleration 1.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 5.55 kg and a = 1.55 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 = 10.85^2 and multiply by 0.5 * 17.9.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1053.6164, "unit": "J"}

Answer: 1053.6164

Prompt: A body of mass 17.9 kg moves at 10.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 10.85^2 and multiply by 0.5 * 17.9.
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=52 degrees through the sine of 2 theta.
3. Substitute v=72.6 m/s and g=9.81 m/s^2.
Final: {"answer": 521.3248, "unit": "m"}

Answer: 521.3248

Prompt: A projectile is launched on level ground with no air resistance at speed 72.6 m/s and angle 52 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=52 degrees through the sine of 2 theta.
Substitute v=72.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.48 * 8.314 * 516 / 8.7.
Final: {"answer": 1716.0096, "unit": "kPa"}

Answer: 1716.0096

Prompt: An ideal gas sample has n=3.48 mol, T=516 K, and V=8.7 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 = 3.48 * 8.314 * 516 / 8.7.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 755 * 1.53 * 8.
Final: {"answer": 9241.2, "unit": "J"}

Answer: 9241.2

Prompt: A 755 g sample has specific heat 1.53 J/(g*K). How much heat is needed to raise its temperature by 8 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 755 * 1.53 * 8.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=14 V and R=128.5 ohm.
Final: {"answer": 1.5253, "unit": "W"}

Answer: 1.5253

Prompt: A resistor has resistance 128.5 ohm and voltage 14 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=14 V and R=128.5 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.78 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1221.4577, "unit": "g"}

Answer: 1221.4577

Prompt: A sample contains 6.78 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 = 6.78 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 3750 mL to 3.75 L.
3. Compute M = 4.495 / 3.75.
Final: {"answer": 1.1987, "unit": "mol/L"}

Answer: 1.1987

Prompt: A solution contains 4.495 mol of solute in 3750 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3750 mL to 3.75 L.
Compute M = 4.495 / 3.75.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 1.28, "unit": "state_units"}

Answer: 1.28

Prompt: Use explicit Euler on dy/dt = -0.85 y with y(0)=12.5, step size h=0.8, 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) = -0.85 y, so each step multiplies y by 1 - h*0.85.
Apply that update for 2 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=0.18 and add it to the current value.
Final: {"answer": [2.248, 0.66, -0.458], "unit": "temperature_units"}

Answer: 2.248

Answer: 0.66

Answer: -0.458

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.7, right=-1.6; current interior values are [2.95, 0.3, -0.35]. Use r=0.18. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.18 and add it to the current value.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 157.5 + 273.15.
Final: {"answer": 430.65, "unit": "K"}

Answer: 430.65

Prompt: Convert 157.5 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 157.5 + 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=229 degrees and keep the unit as newtons.
Final: {"answer": [-244.71, -281.5067], "unit": "N"}

Answer: -244.71

Answer: -281.5067

Prompt: A vector has magnitude 373 N at 229 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=229 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": [-1.25, 30.0], "unit": "dimensionless"}

Answer: -1.25

Answer: 30.0

Prompt: A line passes through points (-9.75, 42.1875) and (0.5, 29.375). 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 quality-control check case 508014, 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_004858(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_004858"}

Answer: python_code

Prompt: Write a Python function threshold_flags_004858(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_004858([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_004858([], 5) == []

assert threshold_flags_004858([-1, 0], 0) == [False, True]


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 3.45 kg and a = 10.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 37.0875, "unit": "N"}

Answer: 37.0875

Prompt: A cart has mass 3.45 kg and measured acceleration 10.75 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 = 3.45 kg and a = 10.75 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=10 degrees through the sine of 2 theta.
3. Substitute v=42.9 m/s and g=9.81 m/s^2.
Final: {"answer": 64.1649, "unit": "m"}

Answer: 64.1649

Prompt: A projectile is launched on level ground with no air resistance at speed 42.9 m/s and angle 10 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=10 degrees through the sine of 2 theta.
Substitute v=42.9 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 = 885 * 2.465 * 55.
Final: {"answer": 119983.875, "unit": "J"}

Answer: 119983.875

Prompt: A 885 g sample has specific heat 2.465 J/(g*K). How much heat is needed to raise its temperature by 55 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 885 * 2.465 * 55.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=25.5 V and R=189.3 ohm.
Final: {"answer": 3.435, "unit": "W"}

Answer: 3.435

Prompt: A resistor has resistance 189.3 ohm and voltage 25.5 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=25.5 V and R=189.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=229 mg, t=137 h, and T_half=67 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 55.5005, "unit": "mg"}

Answer: 55.5005

Prompt: A radioactive sample starts with 229 mg. Its half-life is 67 hours. How many mg remain after 137 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=229 mg, t=137 h, and T_half=67 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 = 1.46 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 64.2546, "unit": "g"}

Answer: 64.2546

Prompt: A sample contains 1.46 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.46 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3955 mL to 3.955 L.
3. Compute M = 3.355 / 3.955.
Final: {"answer": 0.8483, "unit": "mol/L"}

Answer: 0.8483

Prompt: A solution contains 3.355 mol of solute in 3955 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3955 mL to 3.955 L.
Compute M = 3.355 / 3.955.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.64 y with y(0)=1, step size h=1.65, 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) = -0.64 y, so each step multiplies y by 1 - h*0.64.
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(-3.1)=1.91 and f(-0.3)=-12.37.
3. The interval width is 2.8.
Final: {"answer": -14.644, "unit": "area_units"}

Answer: -14.644

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.1x+-13.9 from x=-3.1 to x=-0.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-3.1)=1.91 and f(-0.3)=-12.37.
The interval width is 2.8.


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=0.44 and add it to the current value.
Final: {"answer": [0.434, 2.216, -0.606], "unit": "temperature_units"}

Answer: 0.434

Answer: 2.216

Answer: -0.606

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=-0.95; current interior values are [2.7, -1.15, 2.65]. 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -68.0 + 273.15.
Final: {"answer": 205.15, "unit": "K"}

Answer: 205.15

Prompt: Convert -68 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 -68.0 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=157 degrees and keep the unit as newtons.
Final: {"answer": [-430.7963, 182.8622], "unit": "N"}

Answer: -430.7963

Answer: 182.8622

Prompt: A vector has magnitude 468 N at 157 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=157 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": [-0.05, -29.5], "unit": "dimensionless"}

Answer: -0.05

Answer: -29.5

Prompt: A line passes through points (-1, -29.45) and (3.5, -29.675). 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. speed squared over acceleration has units of meters
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In field worksheet case 728805, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
speed squared over acceleration has units of meters
The equation is valid only if both sides have identical dimensions.

Answer: consistent


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

```python
def center_values_004876(values):
    if not values:
        raise ValueError('center_values requires at least one value')
    mean = sum(values) / len(values)
    return [value - mean for value in values]
```
Final: {"answer": "python_code", "function": "center_values_004876"}

Answer: python_code

Prompt: Write a Python function center_values_004876(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.

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

try:
    center_values_004876([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 30 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 23.3 kg and a = 7.2 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 167.76, "unit": "N"}

Answer: 167.76

Prompt: A cart has mass 23.3 kg and measured acceleration 7.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 23.3 kg and a = 7.2 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 = 45^2 and multiply by 0.5 * 22.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 22275.0, "unit": "J"}

Answer: 22275.0

Prompt: A body of mass 22 kg moves at 45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 45^2 and multiply by 0.5 * 22.
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=57.6 m/s and g=9.81 m/s^2.
Final: {"answer": 137.5591, "unit": "m"}

Answer: 137.5591

Prompt: A projectile is launched on level ground with no air resistance at speed 57.6 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=57.6 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 = 2.9 * 8.314 * 434 / 113.1.
Final: {"answer": 92.5199, "unit": "kPa"}

Answer: 92.5199

Prompt: An ideal gas sample has n=2.9 mol, T=434 K, and V=113.1 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 = 2.9 * 8.314 * 434 / 113.1.