Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=620.5 mg, t=29.5 h, and T_half=118 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 521.7762, "unit": "mg"}

Answer: 521.7762

Prompt: A radioactive sample starts with 620.5 mg. Its half-life is 118 hours. How many mg remain after 29.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=620.5 mg, t=29.5 h, and T_half=118 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


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": [1.05, 16.75], "unit": "dimensionless"}

Answer: 1.05

Answer: 16.75

Prompt: A line passes through points (-9.75, 6.5125) and (-7, 9.4). 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: 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=0.14 and interior values [-1.5, 2.95, -0.8], 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. 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=0.14 and add it to the current value.
Final: {"answer": [0.4, 1.329, 1.169], "unit": "temperature_units"}

Answer: 0.4

Answer: 1.329

Answer: 1.169

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=2.7, right=1.25; current interior values are [-0.3, 1.7, 1.05]. Use r=0.14. 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=0.14 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=208 degrees and keep the unit as newtons.
Final: {"answer": [-82.1141, -43.6609], "unit": "N"}

Answer: -82.1141

Answer: -43.6609

Prompt: A vector has magnitude 93 N at 208 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=208 degrees and keep the unit as newtons.

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


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 = 1.72 * 8.314 * 315 / 41.4.
Final: {"answer": 108.805, "unit": "kPa"}

Answer: 108.805

Prompt: An ideal gas sample has n=1.72 mol, T=315 K, and V=41.4 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 = 1.72 * 8.314 * 315 / 41.4.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 325 mL to 0.325 L.
3. Compute M = 3.185 / 0.325.
Final: {"answer": 9.8, "unit": "mol/L"}

Answer: 9.8

Prompt: A solution contains 3.185 mol of solute in 325 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 325 mL to 0.325 L.
Compute M = 3.185 / 0.325.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1930 * 3.915 * 22.
Final: {"answer": 166230.9, "unit": "J"}

Answer: 166230.9

Prompt: A 1930 g sample has specific heat 3.915 J/(g*K). How much heat is needed to raise its temperature by 22 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1930 * 3.915 * 22.


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=133.5 V and R=56.8 ohm.
Final: {"answer": 313.772, "unit": "W"}

Answer: 313.772

Prompt: A resistor has resistance 56.8 ohm and voltage 133.5 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=133.5 V and R=56.8 ohm.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=280 degrees and keep the unit as newtons.
Final: {"answer": [20.8378, -118.1769], "unit": "N"}

Answer: 20.8378

Answer: -118.1769

Prompt: A vector has magnitude 120 N at 280 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=280 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. velocity divided by time is acceleration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In student derivation case 602167, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
velocity divided by time is acceleration
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 790 * 1.31 * 14.
Final: {"answer": 14488.6, "unit": "J"}

Answer: 14488.6

Prompt: A 790 g sample has specific heat 1.31 J/(g*K). How much heat is needed to raise its temperature by 14 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 790 * 1.31 * 14.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2655 mL to 2.655 L.
3. Compute M = 0.235 / 2.655.
Final: {"answer": 0.0885, "unit": "mol/L"}

Answer: 0.0885

Prompt: A solution contains 0.235 mol of solute in 2655 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2655 mL to 2.655 L.
Compute M = 0.235 / 2.655.


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": [-1.4, -3.25], "unit": "dimensionless"}

Answer: -1.4

Answer: -3.25

Prompt: A line passes through points (-6.5, 5.85) and (-6.25, 5.5). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=78.3 V and R=151.3 ohm.
Final: {"answer": 40.5214, "unit": "W"}

Answer: 40.5214

Prompt: A resistor has resistance 151.3 ohm and voltage 78.3 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=78.3 V and R=151.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=224 mg, t=245 h, and T_half=86 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 31.093, "unit": "mg"}

Answer: 31.093

Prompt: A radioactive sample starts with 224 mg. Its half-life is 86 hours. How many mg remain after 245 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=224 mg, t=245 h, and T_half=86 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.62 y, so each step multiplies y by 1 - h*0.62.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 7.7254, "unit": "state_units"}

Answer: 7.7254

Prompt: Use explicit Euler on dy/dt = -0.62 y with y(0)=53.5, step size h=1, 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) = -0.62 y, so each step multiplies y by 1 - h*0.62.
Apply that update for 2 steps and round the final state.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 14.6747, "unit": "state_units"}

Answer: 14.6747

Prompt: Use explicit Euler on dy/dt = -0.11 y with y(0)=38.5, step size h=1.35, 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) = -0.11 y, so each step multiplies y by 1 - h*0.11.
Apply that update for 6 steps and round the final state.


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=42.7 V and R=153.8 ohm.
Final: {"answer": 11.8549, "unit": "W"}

Answer: 11.8549

Prompt: A resistor has resistance 153.8 ohm and voltage 42.7 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=42.7 V and R=153.8 ohm.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 44000.0 / 1000.
Final: {"answer": 44.0, "unit": "kg"}

Answer: 44.0

Prompt: Convert 44000 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 44000.0 / 1000.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 935 * 0.95 * 70.
Final: {"answer": 62177.5, "unit": "J"}

Answer: 62177.5

Prompt: A 935 g sample has specific heat 0.95 J/(g*K). How much heat is needed to raise its temperature by 70 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 935 * 0.95 * 70.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 194.0 + 273.15.
Final: {"answer": 467.15, "unit": "K"}

Answer: 467.15

Prompt: Convert 194 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 194.0 + 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=192 degrees and keep the unit as newtons.
Final: {"answer": [-40.5931, -8.6283], "unit": "N"}

Answer: -40.5931

Answer: -8.6283

Prompt: A vector has magnitude 41.5 N at 192 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=192 degrees and keep the unit as newtons.


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

Answer: consistent

Prompt: In lab notebook case 992611, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.4 and add it to the current value.
Final: {"answer": [-0.92, -0.38, 0.25], "unit": "temperature_units"}

Answer: -0.92

Answer: -0.38

Answer: 0.25

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.2, right=0.7; current interior values are [-1.4, -0.4, 0.65]. Use r=0.4. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.4 and add it to the current value.


Response:
Reasoning:
1. 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 47 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 Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 290 * 3.22 * 36.
Final: {"answer": 33616.8, "unit": "J"}

Answer: 33616.8

Prompt: A 290 g sample has specific heat 3.22 J/(g*K). How much heat is needed to raise its temperature by 36 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 290 * 3.22 * 36.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=145 mg, t=12.5 h, and T_half=76 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 129.3768, "unit": "mg"}

Answer: 129.3768

Prompt: A radioactive sample starts with 145 mg. Its half-life is 76 hours. How many mg remain after 12.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=145 mg, t=12.5 h, and T_half=76 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1820 * 4.295 * 100.
Final: {"answer": 781690.0, "unit": "J"}

Answer: 781690.0

Prompt: A 1820 g sample has specific heat 4.295 J/(g*K). How much heat is needed to raise its temperature by 100 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1820 * 4.295 * 100.


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=73.2 V and R=117.3 ohm.
Final: {"answer": 45.6798, "unit": "W"}

Answer: 45.6798

Prompt: A resistor has resistance 117.3 ohm and voltage 73.2 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=73.2 V and R=117.3 ohm.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=20 degrees and keep the unit as newtons.
Final: {"answer": [346.2767, 126.0344], "unit": "N"}

Answer: 346.2767

Answer: 126.0344

Prompt: A vector has magnitude 368.5 N at 20 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=20 degrees and keep the unit as newtons.


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

```python
def safe_mean_000268(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_000268"}

Answer: python_code

Prompt: Write a Python function safe_mean_000268(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_000268([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=184 degrees and keep the unit as newtons.
Final: {"answer": [-253.8801, -17.753], "unit": "N"}

Answer: -253.8801

Answer: -17.753

Prompt: A vector has magnitude 254.5 N at 184 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=184 degrees and keep the unit as newtons.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=29 degrees through the sine of 2 theta.
3. Substitute v=19.2 m/s and g=9.81 m/s^2.
Final: {"answer": 31.8679, "unit": "m"}

Answer: 31.8679

Prompt: A projectile is launched on level ground with no air resistance at speed 19.2 m/s and angle 29 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=29 degrees through the sine of 2 theta.
Substitute v=19.2 m/s and g=9.81 m/s^2.

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


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2435 mL to 2.435 L.
3. Compute M = 2.27 / 2.435.
Final: {"answer": 0.9322, "unit": "mol/L"}

Answer: 0.9322

Prompt: A solution contains 2.27 mol of solute in 2435 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2435 mL to 2.435 L.
Compute M = 2.27 / 2.435.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 18.55 kg and a = 13 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 241.15, "unit": "N"}

Answer: 241.15

Prompt: A cart has mass 18.55 kg and measured acceleration 13 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 18.55 kg and a = 13 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 30365.0 / 1000.
Final: {"answer": 30.365, "unit": "kg"}

Answer: 30.365

Prompt: Convert 30365 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 30365.0 / 1000.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 38.9^2 and multiply by 0.5 * 6.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 4993.593, "unit": "J"}

Answer: 4993.593

Prompt: A body of mass 6.6 kg moves at 38.9 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 38.9^2 and multiply by 0.5 * 6.6.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 355 * 0.935 * 89.
Final: {"answer": 29541.325, "unit": "J"}

Answer: 29541.325

Prompt: A 355 g sample has specific heat 0.935 J/(g*K). How much heat is needed to raise its temperature by 89 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 355 * 0.935 * 89.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=108 degrees and keep the unit as newtons.
Final: {"answer": [-9.425, 29.0072], "unit": "N"}

Answer: -9.425

Answer: 29.0072

Prompt: A vector has magnitude 30.5 N at 108 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=108 degrees and keep the unit as newtons.


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 = 2.3 * 8.314 * 344 / 65.7.
Final: {"answer": 100.1223, "unit": "kPa"}

Answer: 100.1223

Prompt: An ideal gas sample has n=2.3 mol, T=344 K, and V=65.7 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 = 2.3 * 8.314 * 344 / 65.7.


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

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid laboratory survey records in release 391537, 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 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 = 4.24 * 8.314 * 470 / 39.2.
Final: {"answer": 422.6566, "unit": "kPa"}

Answer: 422.6566

Prompt: An ideal gas sample has n=4.24 mol, T=470 K, and V=39.2 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 = 4.24 * 8.314 * 470 / 39.2.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=363 mg, t=135 h, and T_half=2.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0, "unit": "mg"}

Answer: 0.0

Prompt: A radioactive sample starts with 363 mg. Its half-life is 2.5 hours. How many mg remain after 135 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=363 mg, t=135 h, and T_half=2.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1030 mL to 1.03 L.
3. Compute M = 4.415 / 1.03.
Final: {"answer": 4.2864, "unit": "mol/L"}

Answer: 4.2864

Prompt: A solution contains 4.415 mol of solute in 1030 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1030 mL to 1.03 L.
Compute M = 4.415 / 1.03.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 12.55 kg and a = 10.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 136.1675, "unit": "N"}

Answer: 136.1675

Prompt: A cart has mass 12.55 kg and measured acceleration 10.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 12.55 kg and a = 10.85 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=234.5 mg, t=188.5 h, and T_half=41 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 9.6859, "unit": "mg"}

Answer: 9.6859

Prompt: A radioactive sample starts with 234.5 mg. Its half-life is 41 hours. How many mg remain after 188.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=234.5 mg, t=188.5 h, and T_half=41 h.
The remaining amount has the same mass unit as the initial amount.


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 registry experiment records in release 206332, 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. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2950 mL to 2.95 L.
3. Compute M = 4.21 / 2.95.
Final: {"answer": 1.4271, "unit": "mol/L"}

Answer: 1.4271

Prompt: A solution contains 4.21 mol of solute in 2950 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2950 mL to 2.95 L.
Compute M = 4.21 / 2.95.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3724.0 / 100.
Final: {"answer": 37.24, "unit": "m"}

Answer: 37.24

Prompt: Convert 3724 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 3724.0 / 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": [6.45, 17.75], "unit": "dimensionless"}

Answer: 6.45

Answer: 17.75

Prompt: A line passes through points (-18.5, -101.575) and (-14.5, -75.775). Return [slope, intercept] for y = slope*x + intercept.

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


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

```python
def running_total_000466(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_000466"}

Answer: python_code

Prompt: Write a Python function running_total_000466(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 24.45 kg and a = 8.9 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 217.605, "unit": "N"}

Answer: 217.605

Prompt: A cart has mass 24.45 kg and measured acceleration 8.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 24.45 kg and a = 8.9 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1395 * 1.745 * 16.
Final: {"answer": 38948.4, "unit": "J"}

Answer: 38948.4

Prompt: A 1395 g sample has specific heat 1.745 J/(g*K). How much heat is needed to raise its temperature by 16 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1395 * 1.745 * 16.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1280 mL to 1.28 L.
3. Compute M = 2.365 / 1.28.
Final: {"answer": 1.8477, "unit": "mol/L"}

Answer: 1.8477

Prompt: A solution contains 2.365 mol of solute in 1280 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1280 mL to 1.28 L.
Compute M = 2.365 / 1.28.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 2.65 kg and a = 3.15 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 8.3475, "unit": "N"}

Answer: 8.3475

Prompt: A cart has mass 2.65 kg and measured acceleration 3.15 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 = 2.65 kg and a = 3.15 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1690 * 4.245 * 67.
Final: {"answer": 480661.35, "unit": "J"}

Answer: 480661.35

Prompt: A 1690 g sample has specific heat 4.245 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 = 1690 * 4.245 * 67.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=339 degrees and keep the unit as newtons.
Final: {"answer": [202.587, -77.7658], "unit": "N"}

Answer: 202.587

Answer: -77.7658

Prompt: A vector has magnitude 217 N at 339 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=339 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 38.85^2 and multiply by 0.5 * 27.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 20375.8538, "unit": "J"}

Answer: 20375.8538

Prompt: A body of mass 27 kg moves at 38.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 38.85^2 and multiply by 0.5 * 27.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=317.5 mg, t=305.5 h, and T_half=84 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 25.5227, "unit": "mg"}

Answer: 25.5227

Prompt: A radioactive sample starts with 317.5 mg. Its half-life is 84 hours. How many mg remain after 305.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=317.5 mg, t=305.5 h, and T_half=84 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.32 and add it to the current value.
Final: {"answer": [-1.114, -0.086, 0.524], "unit": "temperature_units"}

Answer: -1.114

Answer: -0.086

Answer: 0.524

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=0.85; current interior values are [-0.65, -1.35, 1.9]. Use r=0.32. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.32 and add it to the current value.


Response:
Reasoning:
1. The 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_000538(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_000538"}

Answer: python_code

Prompt: Write a Python function running_total_000538(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

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


Response:
Reasoning:
1. Use 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 = 1.12 * 8.314 * 478 / 61.2.
Final: {"answer": 72.7285, "unit": "kPa"}

Answer: 72.7285

Prompt: An ideal gas sample has n=1.12 mol, T=478 K, and V=61.2 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 = 1.12 * 8.314 * 478 / 61.2.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=21.3 V and R=18.9 ohm.
Final: {"answer": 24.0048, "unit": "W"}

Answer: 24.0048

Prompt: A resistor has resistance 18.9 ohm and voltage 21.3 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=21.3 V and R=18.9 ohm.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1165 * 0.545 * 91.
Final: {"answer": 57778.175, "unit": "J"}

Answer: 57778.175

Prompt: A 1165 g sample has specific heat 0.545 J/(g*K). How much heat is needed to raise its temperature by 91 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1165 * 0.545 * 91.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1460 * 4.03 * 92.
Final: {"answer": 541309.6, "unit": "J"}

Answer: 541309.6

Prompt: A 1460 g sample has specific heat 4.03 J/(g*K). How much heat is needed to raise its temperature by 92 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1460 * 4.03 * 92.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=6 degrees through the sine of 2 theta.
3. Substitute v=22.3 m/s and g=9.81 m/s^2.
Final: {"answer": 10.5395, "unit": "m"}

Answer: 10.5395

Prompt: A projectile is launched on level ground with no air resistance at speed 22.3 m/s and angle 6 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=6 degrees through the sine of 2 theta.
Substitute v=22.3 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 = 5.7 * 8.314 * 574 / 51.4.
Final: {"answer": 529.2168, "unit": "kPa"}

Answer: 529.2168

Prompt: An ideal gas sample has n=5.7 mol, T=574 K, and V=51.4 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 = 5.7 * 8.314 * 574 / 51.4.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4625 mL to 4.625 L.
3. Compute M = 1.22 / 4.625.
Final: {"answer": 0.2638, "unit": "mol/L"}

Answer: 0.2638

Prompt: A solution contains 1.22 mol of solute in 4625 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4625 mL to 4.625 L.
Compute M = 1.22 / 4.625.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 31510.0 / 1000.
Final: {"answer": 31.51, "unit": "kg"}

Answer: 31.51

Prompt: Convert 31510 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 31510.0 / 1000.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [9.65, 26.0], "unit": "dimensionless"}

Answer: 9.65

Answer: 26.0

Prompt: A line passes through points (10.5, 127.325) and (21, 228.65). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In student derivation case 490018, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. 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 ledger records in release 808203, 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. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: required_fields, allowed_transformations.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid mobile survey records in release 881427, 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 = 5.6 kg and a = 7.4 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 41.44, "unit": "N"}

Answer: 41.44

Prompt: A cart has mass 5.6 kg and measured acceleration 7.4 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 = 5.6 kg and a = 7.4 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=816.5 mg, t=324.5 h, and T_half=7.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0, "unit": "mg"}

Answer: 0.0

Prompt: A radioactive sample starts with 816.5 mg. Its half-life is 7.5 hours. How many mg remain after 324.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=816.5 mg, t=324.5 h, and T_half=7.5 h.
The remaining amount has the same mass unit as the initial amount.


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

Answer: inconsistent

Prompt: In model card equation case 567911, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 24.1 kg and a = 5.05 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 121.705, "unit": "N"}

Answer: 121.705

Prompt: A cart has mass 24.1 kg and measured acceleration 5.05 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 = 24.1 kg and a = 5.05 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1485 mL to 1.485 L.
3. Compute M = 4.03 / 1.485.
Final: {"answer": 2.7138, "unit": "mol/L"}

Answer: 2.7138

Prompt: A solution contains 4.03 mol of solute in 1485 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1485 mL to 1.485 L.
Compute M = 4.03 / 1.485.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.06 and add it to the current value.
Final: {"answer": [-0.129, -0.218, -0.427], "unit": "temperature_units"}

Answer: -0.129

Answer: -0.218

Answer: -0.427

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.45, right=-1.05; current interior values are [-0.3, -0.2, -0.4]. Use r=0.06. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.06 and add it to the current value.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.65 y, so each step multiplies y by 1 - h*0.65.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.65 y with y(0)=59, step size h=1.3, for 11 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.65 y, so each step multiplies y by 1 - h*0.65.
Apply that update for 11 steps and round the final state.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=55.5 mg, t=85.5 h, and T_half=108 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 32.061, "unit": "mg"}

Answer: 32.061

Prompt: A radioactive sample starts with 55.5 mg. Its half-life is 108 hours. How many mg remain after 85.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=55.5 mg, t=85.5 h, and T_half=108 h.
The remaining amount has the same mass unit as the initial amount.


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

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each registry experiment record from batch 728106 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. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.63 y with y(0)=8, step size h=1.5, 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) = -0.63 y, so each step multiplies y by 1 - h*0.63.
Apply that update for 5 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.06 and add it to the current value.
Final: {"answer": [-0.76, -0.73, 0.727], "unit": "temperature_units"}

Answer: -0.76

Answer: -0.73

Answer: 0.727

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=-1.55, right=-1.7; current interior values are [-0.7, -0.85, 1.0]. Use r=0.06. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.06 and add it to the current value.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 103.5 + 273.15.
Final: {"answer": 376.65, "unit": "K"}

Answer: 376.65

Prompt: Convert 103.5 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 103.5 + 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=7 degrees and keep the unit as newtons.
Final: {"answer": [199.5018, 24.4957], "unit": "N"}

Answer: 199.5018

Answer: 24.4957

Prompt: A vector has magnitude 201 N at 7 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=7 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1585 * 3.755 * 62.
Final: {"answer": 369003.85, "unit": "J"}

Answer: 369003.85

Prompt: A 1585 g sample has specific heat 3.755 J/(g*K). How much heat is needed to raise its temperature by 62 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1585 * 3.755 * 62.


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=0.14 and interior values [1.6, -0.75, -1.65], 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 = 24.15 kg and a = 3.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 95.3925, "unit": "N"}

Answer: 95.3925

Prompt: A cart has mass 24.15 kg and measured acceleration 3.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 24.15 kg and a = 3.95 m/s^2.
The unit kg*m/s^2 is one newton.


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 = 1.24 * 8.314 * 276 / 114.8.
Final: {"answer": 24.7856, "unit": "kPa"}

Answer: 24.7856

Prompt: An ideal gas sample has n=1.24 mol, T=276 K, and V=114.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.24 * 8.314 * 276 / 114.8.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 630 mL to 0.63 L.
3. Compute M = 0.075 / 0.63.
Final: {"answer": 0.119, "unit": "mol/L"}

Answer: 0.119

Prompt: A solution contains 0.075 mol of solute in 630 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 630 mL to 0.63 L.
Compute M = 0.075 / 0.63.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-9.8)=-78.86 and f(-6.1)=-52.22.
3. The interval width is 3.7.
Final: {"answer": -242.498, "unit": "area_units"}

Answer: -242.498

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.2x+-8.3 from x=-9.8 to x=-6.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.8)=-78.86 and f(-6.1)=-52.22.
The interval width is 3.7.

(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=0.1 and add it to the current value.
Final: {"answer": [-1.66, -1.245, -0.145], "unit": "temperature_units"}

Answer: -1.66

Answer: -1.245

Answer: -0.145

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=0.7, right=0.25; current interior values are [-2.0, -1.3, -0.05]. Use r=0.1. Return the next interior vector.

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


Response:
Reasoning:
1. The 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_000826(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_000826"}

Answer: python_code

Prompt: Write a Python function finite_differences_000826(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_000826([5]) == []

assert finite_differences_000826([]) == []


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=37 degrees through the sine of 2 theta.
3. Substitute v=54.5 m/s and g=9.81 m/s^2.
Final: {"answer": 291.0487, "unit": "m"}

Answer: 291.0487

Prompt: A projectile is launched on level ground with no air resistance at speed 54.5 m/s and angle 37 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=37 degrees through the sine of 2 theta.
Substitute v=54.5 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 = 995 * 1.705 * 34.
Final: {"answer": 57680.15, "unit": "J"}

Answer: 57680.15

Prompt: A 995 g sample has specific heat 1.705 J/(g*K). How much heat is needed to raise its temperature by 34 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 995 * 1.705 * 34.


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_000844(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_000844"}

Answer: python_code

Prompt: Write a Python function weighted_sum_000844(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_000844([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1540.0 / 100.
Final: {"answer": 15.4, "unit": "m"}

Answer: 15.4

Prompt: Convert 1540 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 1540.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=318 degrees and keep the unit as newtons.
Final: {"answer": [23.4091, -21.0776], "unit": "N"}

Answer: 23.4091

Answer: -21.0776

Prompt: A vector has magnitude 31.5 N at 318 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=318 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [4.3, -26.75], "unit": "dimensionless"}

Answer: 4.3

Answer: -26.75

Prompt: A line passes through points (9, 11.95) and (20.75, 62.475). 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. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=291 degrees and keep the unit as newtons.
Final: {"answer": [94.0716, -245.0649], "unit": "N"}

Answer: 94.0716

Answer: -245.0649

Prompt: A vector has magnitude 262.5 N at 291 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=291 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.21 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 21.7981, "unit": "g"}

Answer: 21.7981

Prompt: A sample contains 1.21 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.21 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


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 = 1.67 * 8.314 * 546 / 109.1.
Final: {"answer": 69.4855, "unit": "kPa"}

Answer: 69.4855

Prompt: An ideal gas sample has n=1.67 mol, T=546 K, and V=109.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.67 * 8.314 * 546 / 109.1.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=123 degrees and keep the unit as newtons.
Final: {"answer": [-98.5797, 151.7994], "unit": "N"}

Answer: -98.5797

Answer: 151.7994

Prompt: A vector has magnitude 181 N at 123 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=123 degrees and keep the unit as newtons.


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

```python
def normalize_000934(values):
    total = sum(values)
    if total == 0:
        raise ValueError('cannot normalize zero-sum values')
    return [v / total for v in values]
```
Final: {"answer": "python_code", "function": "normalize_000934"}

Answer: python_code

Prompt: Write a Python function normalize_000934(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.

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

out = normalize_000934([2, 3, 5]); assert len(out) == 3

try:
    normalize_000934([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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 = 4.96 * 8.314 * 241 / 93.3.
Final: {"answer": 106.519, "unit": "kPa"}

Answer: 106.519

Prompt: An ideal gas sample has n=4.96 mol, T=241 K, and V=93.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.96 * 8.314 * 241 / 93.3.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 28.0 + 273.15.
Final: {"answer": 301.15, "unit": "K"}

Answer: 301.15

Prompt: Convert 28 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 28.0 + 273.15.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 23.4^2 and multiply by 0.5 * 21.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5831.514, "unit": "J"}

Answer: 5831.514

Prompt: A body of mass 21.3 kg moves at 23.4 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 23.4^2 and multiply by 0.5 * 21.3.
The unit kg*m^2/s^2 is one joule.


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 registry survey records in release 360149, 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. Mass equals amount in moles times molar mass.
2. Use m = 4.06 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 731.4334, "unit": "g"}

Answer: 731.4334

Prompt: A sample contains 4.06 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.06 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.46 * 8.314 * 342 / 115.3.
Final: {"answer": 134.6479, "unit": "kPa"}

Answer: 134.6479

Prompt: An ideal gas sample has n=5.46 mol, T=342 K, and V=115.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.46 * 8.314 * 342 / 115.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 390 * 0.53 * 41.
Final: {"answer": 8474.7, "unit": "J"}

Answer: 8474.7

Prompt: A 390 g sample has specific heat 0.53 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 = 390 * 0.53 * 41.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=82 mg, t=12 h, and T_half=2.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 2.9435, "unit": "mg"}

Answer: 2.9435

Prompt: A radioactive sample starts with 82 mg. Its half-life is 2.5 hours. How many mg remain after 12 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=82 mg, t=12 h, and T_half=2.5 h.
The remaining amount has the same mass unit as the initial amount.


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 lab notebook case 548293, 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 x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=131 degrees and keep the unit as newtons.
Final: {"answer": [-27.8825, 32.0752], "unit": "N"}

Answer: -27.8825

Answer: 32.0752

Prompt: A vector has magnitude 42.5 N at 131 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=131 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. volt squared divided by ohm is watt
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In simulation spec case 616841, 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 x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=115 degrees and keep the unit as newtons.
Final: {"answer": [-130.589, 280.0491], "unit": "N"}

Answer: -130.589

Answer: 280.0491

Prompt: A vector has magnitude 309 N at 115 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=115 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.87 * 8.314 * 373 / 17.8.
Final: {"answer": 1022.6734, "unit": "kPa"}

Answer: 1022.6734

Prompt: An ideal gas sample has n=5.87 mol, T=373 K, and V=17.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.87 * 8.314 * 373 / 17.8.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.97 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 97.0844, "unit": "g"}

Answer: 97.0844

Prompt: A sample contains 0.97 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.97 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


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

```python
import math

def unit_vector_001096(x, y):
    norm = math.hypot(x, y)
    if norm == 0:
        raise ValueError('zero vector has no direction')
    return (x / norm, y / norm)
```
Final: {"answer": "python_code", "function": "unit_vector_001096"}

Answer: python_code

Prompt: Write a Python function unit_vector_001096(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.

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

try:
    unit_vector_001096(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.69 y, so each step multiplies y by 1 - h*0.69.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 2.3764, "unit": "state_units"}

Answer: 2.3764

Prompt: Use explicit Euler on dy/dt = -0.69 y with y(0)=16.5, step size h=0.4, 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) = -0.69 y, so each step multiplies y by 1 - h*0.69.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3185 mL to 3.185 L.
3. Compute M = 4.875 / 3.185.
Final: {"answer": 1.5306, "unit": "mol/L"}

Answer: 1.5306

Prompt: A solution contains 4.875 mol of solute in 3185 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3185 mL to 3.185 L.
Compute M = 4.875 / 3.185.


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_001132(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_001132"}

Answer: python_code

Prompt: Write a Python function safe_mean_001132(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_001132([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(1.7)=14.88 and f(7.6)=11.34.
3. The interval width is 5.9.
Final: {"answer": 77.349, "unit": "area_units"}

Answer: 77.349

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.6x+15.9 from x=1.7 to x=7.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.7)=14.88 and f(7.6)=11.34.
The interval width is 5.9.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=85 degrees through the sine of 2 theta.
3. Substitute v=61.3 m/s and g=9.81 m/s^2.
Final: {"answer": 66.5154, "unit": "m"}

Answer: 66.5154

Prompt: A projectile is launched on level ground with no air resistance at speed 61.3 m/s and angle 85 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=85 degrees through the sine of 2 theta.
Substitute v=61.3 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 = 2.58 * 8.314 * 501 / 3.0.
Final: {"answer": 3582.17, "unit": "kPa"}

Answer: 3582.17

Prompt: An ideal gas sample has n=2.58 mol, T=501 K, and V=3.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.58 * 8.314 * 501 / 3.0.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-7.8)=-19.66 and f(-1.9)=5.12.
3. The interval width is 5.9.
Final: {"answer": -42.893, "unit": "area_units"}

Answer: -42.893

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.2x+13.1 from x=-7.8 to x=-1.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.8)=-19.66 and f(-1.9)=5.12.
The interval width is 5.9.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=80 degrees and keep the unit as newtons.
Final: {"answer": [57.9117, 328.4334], "unit": "N"}

Answer: 57.9117

Answer: 328.4334

Prompt: A vector has magnitude 333.5 N at 80 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=80 degrees and keep the unit as newtons.


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 warehouse clinical record from batch 745578 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. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.08 and add it to the current value.
Final: {"answer": [-0.156, 2.588, 2.008], "unit": "temperature_units"}

Answer: -0.156

Answer: 2.588

Answer: 2.008

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.65, right=-1.95; current interior values are [-0.4, 2.9, 2.3]. 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. Mass equals amount in moles times molar mass.
2. Use m = 5.23 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 942.2159, "unit": "g"}

Answer: 942.2159

Prompt: A sample contains 5.23 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.23 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


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=212.1 V and R=129.9 ohm.
Final: {"answer": 346.3157, "unit": "W"}

Answer: 346.3157

Prompt: A resistor has resistance 129.9 ohm and voltage 212.1 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=212.1 V and R=129.9 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.62 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 562.4889, "unit": "g"}

Answer: 562.4889

Prompt: A sample contains 5.62 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.62 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 3.85 kg and a = 13.2 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 50.82, "unit": "N"}

Answer: 50.82

Prompt: A cart has mass 3.85 kg and measured acceleration 13.2 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 = 3.85 kg and a = 13.2 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 4.2 kg and a = 12.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 52.92, "unit": "N"}

Answer: 52.92

Prompt: A cart has mass 4.2 kg and measured acceleration 12.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 4.2 kg and a = 12.6 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.3 and add it to the current value.
Final: {"answer": [0.48, -0.12, -0.325], "unit": "temperature_units"}

Answer: 0.48

Answer: -0.12

Answer: -0.325

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=2.4; current interior values are [3.0, -1.35, -1.6]. Use r=0.3. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=91 degrees and keep the unit as newtons.
Final: {"answer": [-5.5237, 316.4518], "unit": "N"}

Answer: -5.5237

Answer: 316.4518

Prompt: A vector has magnitude 316.5 N at 91 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=91 degrees and keep the unit as newtons.


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 = 2.94 * 8.314 * 241 / 5.5.
Final: {"answer": 1071.0548, "unit": "kPa"}

Answer: 1071.0548

Prompt: An ideal gas sample has n=2.94 mol, T=241 K, and V=5.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.94 * 8.314 * 241 / 5.5.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=491.5 mg, t=310 h, and T_half=3.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0, "unit": "mg"}

Answer: 0.0

Prompt: A radioactive sample starts with 491.5 mg. Its half-life is 3.5 hours. How many mg remain after 310 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=491.5 mg, t=310 h, and T_half=3.5 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 = 7.02 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 410.2488, "unit": "g"}

Answer: 410.2488

Prompt: A sample contains 7.02 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 = 7.02 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 15.95 kg and a = 12.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 192.995, "unit": "N"}

Answer: 192.995

Prompt: A cart has mass 15.95 kg and measured acceleration 12.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 15.95 kg and a = 12.1 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 40^2 and multiply by 0.5 * 28.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 22680.0, "unit": "J"}

Answer: 22680.0

Prompt: A body of mass 28.35 kg moves at 40 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 and multiply by 0.5 * 28.35.
The unit kg*m^2/s^2 is one joule.


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 billing experiment record from batch 70994 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. Mass equals amount in moles times molar mass.
2. Use m = 1.79 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 32.2469, "unit": "g"}

Answer: 32.2469

Prompt: A sample contains 1.79 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 = 1.79 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(7.4)=-4.26 and f(16.4)=-21.36.
3. The interval width is 9.
Final: {"answer": -115.29, "unit": "area_units"}

Answer: -115.29

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.9x+9.8 from x=7.4 to x=16.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7.4)=-4.26 and f(16.4)=-21.36.
The interval width is 9.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [3.65, -5.75], "unit": "dimensionless"}

Answer: 3.65

Answer: -5.75

Prompt: A line passes through points (-8.75, -37.6875) and (6.25, 17.0625). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 2.15^2 and multiply by 0.5 * 28.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 66.3329, "unit": "J"}

Answer: 66.3329

Prompt: A body of mass 28.7 kg moves at 2.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 2.15^2 and multiply by 0.5 * 28.7.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=60.1 V and R=192.8 ohm.
Final: {"answer": 18.7345, "unit": "W"}

Answer: 18.7345

Prompt: A resistor has resistance 192.8 ohm and voltage 60.1 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=60.1 V and R=192.8 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.54 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 440.6376, "unit": "g"}

Answer: 440.6376

Prompt: A sample contains 7.54 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 = 7.54 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.4 and add it to the current value.
Final: {"answer": [0.78, -0.44, -0.33], "unit": "temperature_units"}

Answer: 0.78

Answer: -0.44

Answer: -0.33

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 [-1.3, 0.9, -0.25]. Use r=0.4. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.4 and add it to the current value.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 15.25 kg and a = 12.15 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 185.2875, "unit": "N"}

Answer: 185.2875

Prompt: A cart has mass 15.25 kg and measured acceleration 12.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 15.25 kg and a = 12.15 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 31.1^2 and multiply by 0.5 * 10.4.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5029.492, "unit": "J"}

Answer: 5029.492

Prompt: A body of mass 10.4 kg moves at 31.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 31.1^2 and multiply by 0.5 * 10.4.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 193.0 + 273.15.
Final: {"answer": 466.15, "unit": "K"}

Answer: 466.15

Prompt: Convert 193 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 193.0 + 273.15.


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=17.9 V and R=84.1 ohm.
Final: {"answer": 3.8099, "unit": "W"}

Answer: 3.8099

Prompt: A resistor has resistance 84.1 ohm and voltage 17.9 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=17.9 V and R=84.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=644.5 mg, t=119 h, and T_half=60 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 162.9972, "unit": "mg"}

Answer: 162.9972

Prompt: A radioactive sample starts with 644.5 mg. Its half-life is 60 hours. How many mg remain after 119 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=644.5 mg, t=119 h, and T_half=60 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-4.55, 5.75], "unit": "dimensionless"}

Answer: -4.55

Answer: 5.75

Prompt: A line passes through points (1.75, -2.2125) and (2.25, -4.4875). 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: 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 field sensor record from batch 91633 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. 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=24.1 m/s and g=9.81 m/s^2.
Final: {"answer": 47.8986, "unit": "m"}

Answer: 47.8986

Prompt: A projectile is launched on level ground with no air resistance at speed 24.1 m/s and angle 27 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=27 degrees through the sine of 2 theta.
Substitute v=24.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=631 mg, t=320 h, and T_half=14 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0001, "unit": "mg"}

Answer: 0.0001

Prompt: A radioactive sample starts with 631 mg. Its half-life is 14 hours. How many mg remain after 320 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=631 mg, t=320 h, and T_half=14 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 = 7.64 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 336.2364, "unit": "g"}

Answer: 336.2364

Prompt: A sample contains 7.64 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.64 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.32 and add it to the current value.
Final: {"answer": [1.35, 1.314, 0.646], "unit": "temperature_units"}

Answer: 1.35

Answer: 1.314

Answer: 0.646

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=-0.75; current interior values are [1.35, 1.25, 1.35]. Use r=0.32. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.32 and add it to the current value.


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

```python
def normalize_001456(values):
    total = sum(values)
    if total == 0:
        raise ValueError('cannot normalize zero-sum values')
    return [v / total for v in values]
```
Final: {"answer": "python_code", "function": "normalize_001456"}

Answer: python_code

Prompt: Write a Python function normalize_001456(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.

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

out = normalize_001456([2, 3, 5]); assert len(out) == 3

try:
    normalize_001456([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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": [-0.965, -0.069, -0.785], "unit": "temperature_units"}

Answer: -0.965

Answer: -0.069

Answer: -0.785

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=-0.1; current interior values are [1.45, -1.35, -1.1]. 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=314 degrees and keep the unit as newtons.
Final: {"answer": [331.6994, -343.4848], "unit": "N"}

Answer: 331.6994

Answer: -343.4848

Prompt: A vector has magnitude 477.5 N at 314 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=314 degrees and keep the unit as newtons.


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

```python
def weighted_sum_001492(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_001492"}

Answer: python_code

Prompt: Write a Python function weighted_sum_001492(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_001492([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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": [-5.7, -17.0], "unit": "dimensionless"}

Answer: -5.7

Answer: -17.0

Prompt: A line passes through points (6.5, -54.05) and (21.5, -139.55). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 4.15 kg and a = 8.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 36.3125, "unit": "N"}

Answer: 36.3125

Prompt: A cart has mass 4.15 kg and measured acceleration 8.75 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 = 4.15 kg and a = 8.75 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 22.6^2 and multiply by 0.5 * 11.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3013.484, "unit": "J"}

Answer: 3013.484

Prompt: A body of mass 11.8 kg moves at 22.6 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 22.6^2 and multiply by 0.5 * 11.8.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.53 y, so each step multiplies y by 1 - h*0.53.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 3.5219, "unit": "state_units"}

Answer: 3.5219

Prompt: Use explicit Euler on dy/dt = -0.53 y with y(0)=35, step size h=0.6, 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) = -0.53 y, so each step multiplies y by 1 - h*0.53.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 45194.0 / 1000.
Final: {"answer": 45.194, "unit": "kg"}

Answer: 45.194

Prompt: Convert 45194 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 45194.0 / 1000.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 26.45^2 and multiply by 0.5 * 19.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 6716.184, "unit": "J"}

Answer: 6716.184

Prompt: A body of mass 19.2 kg moves at 26.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 26.45^2 and multiply by 0.5 * 19.2.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=14 degrees through the sine of 2 theta.
3. Substitute v=59.3 m/s and g=9.81 m/s^2.
Final: {"answer": 168.2867, "unit": "m"}

Answer: 168.2867

Prompt: A projectile is launched on level ground with no air resistance at speed 59.3 m/s and angle 14 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=14 degrees through the sine of 2 theta.
Substitute v=59.3 m/s and g=9.81 m/s^2.


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_001582(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_001582"}

Answer: python_code

Prompt: Write a Python function safe_mean_001582(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_001582([])
    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 63.7 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.