Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(1.9)=-10.49 and f(2.1)=-11.31.
3. The interval width is 0.2.
Final: {"answer": -2.18, "unit": "area_units"}

Answer: -2.18

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.1x+-2.7 from x=1.9 to x=2.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.9)=-10.49 and f(2.1)=-11.31.
The interval width is 0.2.


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=0.24 and add it to the current value.
Final: {"answer": [0.83, 0.644, -0.312], "unit": "temperature_units"}

Answer: 0.83

Answer: 0.644

Answer: -0.312

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=-0.05, right=-1.45; current interior values are [1.25, 0.8, -0.3]. Use r=0.24. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.24 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 2887.5 / 100.
Final: {"answer": 28.875, "unit": "m"}

Answer: 28.875

Prompt: Convert 2887.5 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 2887.5 / 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": [-8.05, -20.0], "unit": "dimensionless"}

Answer: -8.05

Answer: -20.0

Prompt: A line passes through points (-11, 68.55) and (1.75, -34.0875). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In field worksheet case 264683, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
import math

def unit_vector_006262(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_006262"}

Answer: python_code

Prompt: Write a Python function unit_vector_006262(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_006262(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 877521, 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 = 9.65 kg and a = 15.8 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 152.47, "unit": "N"}

Answer: 152.47

Prompt: A cart has mass 9.65 kg and measured acceleration 15.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 9.65 kg and a = 15.8 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 = 31.95^2 and multiply by 0.5 * 24.65.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 12581.3908, "unit": "J"}

Answer: 12581.3908

Prompt: A body of mass 24.65 kg moves at 31.95 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 31.95^2 and multiply by 0.5 * 24.65.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.66 * 8.314 * 250 / 82.6.
Final: {"answer": 66.9347, "unit": "kPa"}

Answer: 66.9347

Prompt: An ideal gas sample has n=2.66 mol, T=250 K, and V=82.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.66 * 8.314 * 250 / 82.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1810 * 3.41 * 3.
Final: {"answer": 18516.3, "unit": "J"}

Answer: 18516.3

Prompt: A 1810 g sample has specific heat 3.41 J/(g*K). How much heat is needed to raise its temperature by 3 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1810 * 3.41 * 3.


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=100.3 ohm.
Final: {"answer": 4.5233, "unit": "W"}

Answer: 4.5233

Prompt: A resistor has resistance 100.3 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=100.3 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.77 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 395.6388, "unit": "g"}

Answer: 395.6388

Prompt: A sample contains 6.77 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.77 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3455 mL to 3.455 L.
3. Compute M = 2.54 / 3.455.
Final: {"answer": 0.7352, "unit": "mol/L"}

Answer: 0.7352

Prompt: A solution contains 2.54 mol of solute in 3455 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3455 mL to 3.455 L.
Compute M = 2.54 / 3.455.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.61 y, so each step multiplies y by 1 - h*0.61.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.61 y with y(0)=58.5, step size h=1.8, for 9 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.61 y, so each step multiplies y by 1 - h*0.61.
Apply that update for 9 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=0.48 and add it to the current value.
Final: {"answer": [0.042, 1.308, -0.072], "unit": "temperature_units"}

Answer: 0.042

Answer: 1.308

Answer: -0.072

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=1.35, right=1.35; current interior values are [2.85, -1.5, 0.0]. Use r=0.48. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.48 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 31474.0 / 1000.
Final: {"answer": 31.474, "unit": "kg"}

Answer: 31.474

Prompt: Convert 31474 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 31474.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=19 degrees and keep the unit as newtons.
Final: {"answer": [165.4658, 56.9744], "unit": "N"}

Answer: 165.4658

Answer: 56.9744

Prompt: A vector has magnitude 175 N at 19 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=19 degrees and keep the unit as newtons.

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


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-6.9, -20.0], "unit": "dimensionless"}

Answer: -6.9

Answer: -20.0

Prompt: A line passes through points (-0.75, -14.825) and (8.75, -80.375). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In field worksheet case 683720, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 17.65 kg and a = 2.8 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 49.42, "unit": "N"}

Answer: 49.42

Prompt: A cart has mass 17.65 kg and measured acceleration 2.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 17.65 kg and a = 2.8 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 29.25^2 and multiply by 0.5 * 27.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 11806.7625, "unit": "J"}

Answer: 11806.7625

Prompt: A body of mass 27.6 kg moves at 29.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 29.25^2 and multiply by 0.5 * 27.6.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=75 degrees through the sine of 2 theta.
3. Substitute v=28.3 m/s and g=9.81 m/s^2.
Final: {"answer": 40.8201, "unit": "m"}

Answer: 40.8201

Prompt: A projectile is launched on level ground with no air resistance at speed 28.3 m/s and angle 75 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=75 degrees through the sine of 2 theta.
Substitute v=28.3 m/s and g=9.81 m/s^2.

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


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.07 * 8.314 * 504 / 66.0.
Final: {"answer": 67.9329, "unit": "kPa"}

Answer: 67.9329

Prompt: An ideal gas sample has n=1.07 mol, T=504 K, and V=66.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.07 * 8.314 * 504 / 66.0.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=813.5 mg, t=104.5 h, and T_half=44 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 156.8236, "unit": "mg"}

Answer: 156.8236

Prompt: A radioactive sample starts with 813.5 mg. Its half-life is 44 hours. How many mg remain after 104.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=813.5 mg, t=104.5 h, and T_half=44 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.41 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 79.4462, "unit": "g"}

Answer: 79.4462

Prompt: A sample contains 4.41 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 = 4.41 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1220 mL to 1.22 L.
3. Compute M = 0.075 / 1.22.
Final: {"answer": 0.0615, "unit": "mol/L"}

Answer: 0.0615

Prompt: A solution contains 0.075 mol of solute in 1220 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1220 mL to 1.22 L.
Compute M = 0.075 / 1.22.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(6.8)=36.74 and f(11.1)=70.28.
3. The interval width is 4.3.
Final: {"answer": 230.093, "unit": "area_units"}

Answer: 230.093

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.8x+-16.3 from x=6.8 to x=11.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.8)=36.74 and f(11.1)=70.28.
The interval width is 4.3.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 3569.0 / 1000.
Final: {"answer": 3.569, "unit": "kg"}

Answer: 3.569

Prompt: Convert 3569 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 3569.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=313 degrees and keep the unit as newtons.
Final: {"answer": [104.6867, -112.2628], "unit": "N"}

Answer: 104.6867

Answer: -112.2628

Prompt: A vector has magnitude 153.5 N at 313 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=313 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-7.05, 24.75], "unit": "dimensionless"}

Answer: -7.05

Answer: 24.75

Prompt: A line passes through points (13.25, -68.6625) and (15.25, -82.7625). 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_006298(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_006298"}

Answer: python_code

Prompt: Write a Python function running_total_006298(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 = 8 kg and a = 1.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 13.2, "unit": "N"}

Answer: 13.2

Prompt: A cart has mass 8 kg and measured acceleration 1.65 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 = 8 kg and a = 1.65 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 16.75^2 and multiply by 0.5 * 5.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 785.575, "unit": "J"}

Answer: 785.575

Prompt: A body of mass 5.6 kg moves at 16.75 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 16.75^2 and multiply by 0.5 * 5.6.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=30 degrees through the sine of 2 theta.
3. Substitute v=81 m/s and g=9.81 m/s^2.
Final: {"answer": 579.2041, "unit": "m"}

Answer: 579.2041

Prompt: A projectile is launched on level ground with no air resistance at speed 81 m/s and angle 30 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=30 degrees through the sine of 2 theta.
Substitute v=81 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 = 300 * 0.915 * 36.
Final: {"answer": 9882.0, "unit": "J"}

Answer: 9882.0

Prompt: A 300 g sample has specific heat 0.915 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 = 300 * 0.915 * 36.


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=167.2 V and R=19.6 ohm.
Final: {"answer": 1426.3184, "unit": "W"}

Answer: 1426.3184

Prompt: A resistor has resistance 19.6 ohm and voltage 167.2 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=167.2 V and R=19.6 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=578.5 mg, t=80.5 h, and T_half=110 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 348.3406, "unit": "mg"}

Answer: 348.3406

Prompt: A radioactive sample starts with 578.5 mg. Its half-life is 110 hours. How many mg remain after 80.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=578.5 mg, t=80.5 h, and T_half=110 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.75 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 13.5113, "unit": "g"}

Answer: 13.5113

Prompt: A sample contains 0.75 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.75 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1870 mL to 1.87 L.
3. Compute M = 3.455 / 1.87.
Final: {"answer": 1.8476, "unit": "mol/L"}

Answer: 1.8476

Prompt: A solution contains 3.455 mol of solute in 1870 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1870 mL to 1.87 L.
Compute M = 3.455 / 1.87.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.64 y with y(0)=45, step size h=1.65, 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) = -0.64 y, so each step multiplies y by 1 - h*0.64.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-9.9)=-54.87 and f(-4.7)=-22.11.
3. The interval width is 5.2.
Final: {"answer": -200.148, "unit": "area_units"}

Answer: -200.148

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.3x+7.5 from x=-9.9 to x=-4.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.9)=-54.87 and f(-4.7)=-22.11.
The interval width is 5.2.


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=0.04 and add it to the current value.
Final: {"answer": [0.212, 1.352, -0.834], "unit": "temperature_units"}

Answer: 0.212

Answer: 1.352

Answer: -0.834

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.95, right=-0.5; current interior values are [0.25, 1.5, -0.95]. Use r=0.04. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.04 and add it to the current value.


Response:
Reasoning:
1. 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_006316(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_006316"}

Answer: python_code

Prompt: Write a Python function normalize_006316(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_006316([2, 3, 5]); assert len(out) == 3

try:
    normalize_006316([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 clinical record from batch 701303 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=81 degrees through the sine of 2 theta.
3. Substitute v=56.5 m/s and g=9.81 m/s^2.
Final: {"answer": 100.5565, "unit": "m"}

Answer: 100.5565

Prompt: A projectile is launched on level ground with no air resistance at speed 56.5 m/s and angle 81 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=81 degrees through the sine of 2 theta.
Substitute v=56.5 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.91 * 8.314 * 511 / 6.9.
Final: {"answer": 2407.4573, "unit": "kPa"}

Answer: 2407.4573

Prompt: An ideal gas sample has n=3.91 mol, T=511 K, and V=6.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.91 * 8.314 * 511 / 6.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1925 * 4.165 * 63.
Final: {"answer": 505110.375, "unit": "J"}

Answer: 505110.375

Prompt: A 1925 g sample has specific heat 4.165 J/(g*K). How much heat is needed to raise its temperature by 63 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1925 * 4.165 * 63.


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=145.8 V and R=64.3 ohm.
Final: {"answer": 330.6009, "unit": "W"}

Answer: 330.6009

Prompt: A resistor has resistance 64.3 ohm and voltage 145.8 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=145.8 V and R=64.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=511.5 mg, t=110.5 h, and T_half=22.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 17.0002, "unit": "mg"}

Answer: 17.0002

Prompt: A radioactive sample starts with 511.5 mg. Its half-life is 22.5 hours. How many mg remain after 110.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=511.5 mg, t=110.5 h, and T_half=22.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 220.05, "unit": "g"}

Answer: 220.05

Prompt: A sample contains 5 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 640 mL to 0.64 L.
3. Compute M = 0.21 / 0.64.
Final: {"answer": 0.3281, "unit": "mol/L"}

Answer: 0.3281

Prompt: A solution contains 0.21 mol of solute in 640 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 640 mL to 0.64 L.
Compute M = 0.21 / 0.64.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.37 y, so each step multiplies y by 1 - h*0.37.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 4.6371, "unit": "state_units"}

Answer: 4.6371

Prompt: Use explicit Euler on dy/dt = -0.37 y with y(0)=37.5, step size h=1.1, for 4 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.37 y, so each step multiplies y by 1 - h*0.37.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-1.6)=-16.38 and f(-1.5)=-15.9.
3. The interval width is 0.1.
Final: {"answer": -1.614, "unit": "area_units"}

Answer: -1.614

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.8x+-8.7 from x=-1.6 to x=-1.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-1.6)=-16.38 and f(-1.5)=-15.9.
The interval width is 0.1.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.48 and add it to the current value.
Final: {"answer": [0.282, 1.87, -1.084], "unit": "temperature_units"}

Answer: 0.282

Answer: 1.87

Answer: -1.084

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, right=-1.7; current interior values are [2.85, -0.65, 1.1]. Use r=0.48. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.48 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 648.5 / 100.
Final: {"answer": 6.485, "unit": "m"}

Answer: 6.485

Prompt: Convert 648.5 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 648.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=187 degrees and keep the unit as newtons.
Final: {"answer": [-228.2856, -28.0299], "unit": "N"}

Answer: -228.2856

Answer: -28.0299

Prompt: A vector has magnitude 230 N at 187 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=187 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-5.6, -3.5], "unit": "dimensionless"}

Answer: -5.6

Answer: -3.5

Prompt: A line passes through points (-17.25, 93.1) and (-9.25, 48.3). 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 field worksheet case 961213, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def threshold_flags_006334(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_006334"}

Answer: python_code

Prompt: Write a Python function threshold_flags_006334(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.

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

assert threshold_flags_006334([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_006334([], 5) == []

assert threshold_flags_006334([-1, 0], 0) == [False, True]


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

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a alignment scoring problem with 3123 items and budget 41380, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 21.85^2 and multiply by 0.5 * 10.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2399.0481, "unit": "J"}

Answer: 2399.0481

Prompt: A body of mass 10.05 kg moves at 21.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 21.85^2 and multiply by 0.5 * 10.05.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=35 degrees through the sine of 2 theta.
3. Substitute v=17.5 m/s and g=9.81 m/s^2.
Final: {"answer": 29.3355, "unit": "m"}

Answer: 29.3355

Prompt: A projectile is launched on level ground with no air resistance at speed 17.5 m/s and angle 35 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=35 degrees through the sine of 2 theta.
Substitute v=17.5 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.1 * 8.314 * 443 / 105.6.
Final: {"answer": 108.1214, "unit": "kPa"}

Answer: 108.1214

Prompt: An ideal gas sample has n=3.1 mol, T=443 K, and V=105.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.1 * 8.314 * 443 / 105.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1620 * 1.065 * 73.
Final: {"answer": 125946.9, "unit": "J"}

Answer: 125946.9

Prompt: A 1620 g sample has specific heat 1.065 J/(g*K). How much heat is needed to raise its temperature by 73 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1620 * 1.065 * 73.


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=181.4 V and R=34.4 ohm.
Final: {"answer": 956.5686, "unit": "W"}

Answer: 956.5686

Prompt: A resistor has resistance 34.4 ohm and voltage 181.4 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=181.4 V and R=34.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=277 mg, t=242 h, and T_half=110 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 60.2856, "unit": "mg"}

Answer: 60.2856

Prompt: A radioactive sample starts with 277 mg. Its half-life is 110 hours. How many mg remain after 242 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=277 mg, t=242 h, and T_half=110 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.67 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 337.5567, "unit": "g"}

Answer: 337.5567

Prompt: A sample contains 7.67 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.67 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3430 mL to 3.43 L.
3. Compute M = 3.06 / 3.43.
Final: {"answer": 0.8921, "unit": "mol/L"}

Answer: 0.8921

Prompt: A solution contains 3.06 mol of solute in 3430 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3430 mL to 3.43 L.
Compute M = 3.06 / 3.43.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.78 y with y(0)=20.5, step size h=1.3, for 4 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(4)=32.6 and f(13.9)=70.22.
3. The interval width is 9.9.
Final: {"answer": 508.959, "unit": "area_units"}

Answer: 508.959

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.8x+17.4 from x=4 to x=13.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4)=32.6 and f(13.9)=70.22.
The interval width is 9.9.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.38 and add it to the current value.
Final: {"answer": [0.018, 0.339, 1.154], "unit": "temperature_units"}

Answer: 0.018

Answer: 0.339

Answer: 1.154

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, right=2.4; current interior values are [0.55, 0.7, -0.1]. Use r=0.38. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=142 degrees and keep the unit as newtons.
Final: {"answer": [-238.7673, 186.5454], "unit": "N"}

Answer: -238.7673

Answer: 186.5454

Prompt: A vector has magnitude 303 N at 142 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=142 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": [4.7, -15.5], "unit": "dimensionless"}

Answer: 4.7

Answer: -15.5

Prompt: A line passes through points (-3.75, -33.125) and (5.75, 11.525). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. 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_006352(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_006352"}

Answer: python_code

Prompt: Write a Python function safe_mean_006352(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_006352([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=3.54 mol and T=574 K, but does not give volume. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 3.25 kg and a = 15.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 50.375, "unit": "N"}

Answer: 50.375

Prompt: A cart has mass 3.25 kg and measured acceleration 15.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 3.25 kg and a = 15.5 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 7.45^2 and multiply by 0.5 * 13.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 370.4792, "unit": "J"}

Answer: 370.4792

Prompt: A body of mass 13.35 kg moves at 7.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 7.45^2 and multiply by 0.5 * 13.35.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=39 degrees through the sine of 2 theta.
3. Substitute v=22.9 m/s and g=9.81 m/s^2.
Final: {"answer": 52.2885, "unit": "m"}

Answer: 52.2885

Prompt: A projectile is launched on level ground with no air resistance at speed 22.9 m/s and angle 39 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=39 degrees through the sine of 2 theta.
Substitute v=22.9 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.66 * 8.314 * 243 / 29.5.
Final: {"answer": 182.1696, "unit": "kPa"}

Answer: 182.1696

Prompt: An ideal gas sample has n=2.66 mol, T=243 K, and V=29.5 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 = 2.66 * 8.314 * 243 / 29.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 720 * 0.715 * 69.
Final: {"answer": 35521.2, "unit": "J"}

Answer: 35521.2

Prompt: A 720 g sample has specific heat 0.715 J/(g*K). How much heat is needed to raise its temperature by 69 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 720 * 0.715 * 69.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=68.4 V and R=189.8 ohm.
Final: {"answer": 24.6499, "unit": "W"}

Answer: 24.6499

Prompt: A resistor has resistance 189.8 ohm and voltage 68.4 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=68.4 V and R=189.8 ohm.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3545 mL to 3.545 L.
3. Compute M = 1.61 / 3.545.
Final: {"answer": 0.4542, "unit": "mol/L"}

Answer: 0.4542

Prompt: A solution contains 1.61 mol of solute in 3545 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3545 mL to 3.545 L.
Compute M = 1.61 / 3.545.


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 3 steps and round the final state.
Final: {"answer": 3.4245, "unit": "state_units"}

Answer: 3.4245

Prompt: Use explicit Euler on dy/dt = -0.11 y with y(0)=6, step size h=1.55, for 3 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.
Apply that update for 3 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.12 and add it to the current value.
Final: {"answer": [1.95, 0.56, 1.794], "unit": "temperature_units"}

Answer: 1.95

Answer: 0.56

Answer: 1.794

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, right=2.55; current interior values are [2.4, 0.05, 1.95]. Use r=0.12. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -29.5 + 273.15.
Final: {"answer": 243.65, "unit": "K"}

Answer: 243.65

Prompt: Convert -29.5 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 -29.5 + 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=149 degrees and keep the unit as newtons.
Final: {"answer": [-1.2858, 0.7726], "unit": "N"}

Answer: -1.2858

Answer: 0.7726

Prompt: A vector has magnitude 1.5 N at 149 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=149 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [5.3, 7.5], "unit": "dimensionless"}

Answer: 5.3

Answer: 7.5

Prompt: A line passes through points (13.5, 79.05) and (22.75, 128.075). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In quality-control check case 383727, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def safe_mean_006370(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_006370"}

Answer: python_code

Prompt: Write a Python function safe_mean_006370(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_006370([])
    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 57.5 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. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=60 degrees through the sine of 2 theta.
3. Substitute v=5.6 m/s and g=9.81 m/s^2.
Final: {"answer": 2.7685, "unit": "m"}

Answer: 2.7685

Prompt: A projectile is launched on level ground with no air resistance at speed 5.6 m/s and angle 60 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=60 degrees through the sine of 2 theta.
Substitute v=5.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.81 * 8.314 * 544 / 73.7.
Final: {"answer": 49.708, "unit": "kPa"}

Answer: 49.708

Prompt: An ideal gas sample has n=0.81 mol, T=544 K, and V=73.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.81 * 8.314 * 544 / 73.7.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1720 * 3.71 * 60.
Final: {"answer": 382872.0, "unit": "J"}

Answer: 382872.0

Prompt: A 1720 g sample has specific heat 3.71 J/(g*K). How much heat is needed to raise its temperature by 60 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1720 * 3.71 * 60.


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=167.7 V and R=40.8 ohm.
Final: {"answer": 689.2963, "unit": "W"}

Answer: 689.2963

Prompt: A resistor has resistance 40.8 ohm and voltage 167.7 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=167.7 V and R=40.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=846.5 mg, t=74.5 h, and T_half=35.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 197.646, "unit": "mg"}

Answer: 197.646

Prompt: A radioactive sample starts with 846.5 mg. Its half-life is 35.5 hours. How many mg remain after 74.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=846.5 mg, t=74.5 h, and T_half=35.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.02 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 502.4367, "unit": "g"}

Answer: 502.4367

Prompt: A sample contains 5.02 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.02 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 875 mL to 0.875 L.
3. Compute M = 3.775 / 0.875.
Final: {"answer": 4.3143, "unit": "mol/L"}

Answer: 4.3143

Prompt: A solution contains 3.775 mol of solute in 875 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 875 mL to 0.875 L.
Compute M = 3.775 / 0.875.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.2 y, so each step multiplies y by 1 - h*0.2.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.2116, "unit": "state_units"}

Answer: 0.2116

Prompt: Use explicit Euler on dy/dt = -0.2 y with y(0)=35, step size h=2, for 10 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.2 y, so each step multiplies y by 1 - h*0.2.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(1.8)=9.08 and f(10.4)=14.24.
3. The interval width is 8.6.
Final: {"answer": 100.276, "unit": "area_units"}

Answer: 100.276

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.6x+8 from x=1.8 to x=10.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.8)=9.08 and f(10.4)=14.24.
The interval width is 8.6.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -77.5 + 273.15.
Final: {"answer": 195.65, "unit": "K"}

Answer: 195.65

Prompt: Convert -77.5 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 -77.5 + 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=59 degrees and keep the unit as newtons.
Final: {"answer": [137.0001, 228.0065], "unit": "N"}

Answer: 137.0001

Answer: 228.0065

Prompt: A vector has magnitude 266 N at 59 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=59 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": [4.2, 0.5], "unit": "dimensionless"}

Answer: 4.2

Answer: 0.5

Prompt: A line passes through points (2, 8.9) and (8, 34.1). 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 model card equation case 554753, 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. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.72 * 8.314 * 600 / 50.0.
Final: {"answer": 470.905, "unit": "kPa"}

Answer: 470.905

Prompt: An ideal gas sample has n=4.72 mol, T=600 K, and V=50.0 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 = 4.72 * 8.314 * 600 / 50.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1950 * 1.475 * 53.
Final: {"answer": 152441.25, "unit": "J"}

Answer: 152441.25

Prompt: A 1950 g sample has specific heat 1.475 J/(g*K). How much heat is needed to raise its temperature by 53 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1950 * 1.475 * 53.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=733 mg, t=86 h, and T_half=22 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 48.7922, "unit": "mg"}

Answer: 48.7922

Prompt: A radioactive sample starts with 733 mg. Its half-life is 22 hours. How many mg remain after 86 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=733 mg, t=86 h, and T_half=22 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.95 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 305.8695, "unit": "g"}

Answer: 305.8695

Prompt: A sample contains 6.95 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.95 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2290 mL to 2.29 L.
3. Compute M = 2.57 / 2.29.
Final: {"answer": 1.1223, "unit": "mol/L"}

Answer: 1.1223

Prompt: A solution contains 2.57 mol of solute in 2290 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2290 mL to 2.29 L.
Compute M = 2.57 / 2.29.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 5.244, "unit": "state_units"}

Answer: 5.244

Prompt: Use explicit Euler on dy/dt = -0.42 y with y(0)=19.5, step size h=0.55, 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) = -0.42 y, so each step multiplies y by 1 - h*0.42.
Apply that update for 5 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(4.9)=-18.99 and f(5.6)=-21.86.
3. The interval width is 0.7.
Final: {"answer": -14.2975, "unit": "area_units"}

Answer: -14.2975

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.1x+1.1 from x=4.9 to x=5.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.9)=-18.99 and f(5.6)=-21.86.
The interval width is 0.7.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.02 and add it to the current value.
Final: {"answer": [2.451, -0.977, -1.01], "unit": "temperature_units"}

Answer: 2.451

Answer: -0.977

Answer: -1.01

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=0.95; current interior values are [2.6, -1.05, -1.05]. Use r=0.02. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.02 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 28739.0 / 1000.
Final: {"answer": 28.739, "unit": "kg"}

Answer: 28.739

Prompt: Convert 28739 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 28739.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=247 degrees and keep the unit as newtons.
Final: {"answer": [-22.467, -52.929], "unit": "N"}

Answer: -22.467

Answer: -52.929

Prompt: A vector has magnitude 57.5 N at 247 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=247 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-5.9, 10.0], "unit": "dimensionless"}

Answer: -5.9

Answer: 10.0

Prompt: A line passes through points (17.5, -93.25) and (28.5, -158.15). 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=0.28 and interior values [0.15, -1.05, 2.45], 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 = 12.9 kg and a = 3.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 39.99, "unit": "N"}

Answer: 39.99

Prompt: A cart has mass 12.9 kg and measured acceleration 3.1 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 = 12.9 kg and a = 3.1 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 = 42.85^2 and multiply by 0.5 * 23.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 21253.1179, "unit": "J"}

Answer: 21253.1179

Prompt: A body of mass 23.15 kg moves at 42.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 42.85^2 and multiply by 0.5 * 23.15.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=57 degrees through the sine of 2 theta.
3. Substitute v=54.6 m/s and g=9.81 m/s^2.
Final: {"answer": 277.6172, "unit": "m"}

Answer: 277.6172

Prompt: A projectile is launched on level ground with no air resistance at speed 54.6 m/s and angle 57 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=57 degrees through the sine of 2 theta.
Substitute v=54.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.73 * 8.314 * 334 / 33.8.
Final: {"answer": 224.2861, "unit": "kPa"}

Answer: 224.2861

Prompt: An ideal gas sample has n=2.73 mol, T=334 K, and V=33.8 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 = 2.73 * 8.314 * 334 / 33.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1665 * 4.675 * 1.
Final: {"answer": 7783.875, "unit": "J"}

Answer: 7783.875

Prompt: A 1665 g sample has specific heat 4.675 J/(g*K). How much heat is needed to raise its temperature by 1 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1665 * 4.675 * 1.


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=75.9 V and R=118.6 ohm.
Final: {"answer": 48.5734, "unit": "W"}

Answer: 48.5734

Prompt: A resistor has resistance 118.6 ohm and voltage 75.9 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=75.9 V and R=118.6 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.86 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 50.2584, "unit": "g"}

Answer: 50.2584

Prompt: A sample contains 0.86 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.86 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 50 mL to 0.05 L.
3. Compute M = 2.85 / 0.05.
Final: {"answer": 57.0, "unit": "mol/L"}

Answer: 57.0

Prompt: A solution contains 2.85 mol of solute in 50 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 50 mL to 0.05 L.
Compute M = 2.85 / 0.05.


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 5 steps and round the final state.
Final: {"answer": 0.0001, "unit": "state_units"}

Answer: 0.0001

Prompt: Use explicit Euler on dy/dt = -0.53 y with y(0)=53.5, step size h=1.75, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.53 y, so each step multiplies y by 1 - h*0.53.
Apply that update for 5 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(2)=-13.1 and f(9.7)=-65.46.
3. The interval width is 7.7.
Final: {"answer": -302.456, "unit": "area_units"}

Answer: -302.456

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.8x+0.5 from x=2 to x=9.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(2)=-13.1 and f(9.7)=-65.46.
The interval width is 7.7.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.44 and add it to the current value.
Final: {"answer": [0.676, 1.328, -0.488], "unit": "temperature_units"}

Answer: 0.676

Answer: 1.328

Answer: -0.488

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=2.65, right=-0.35; current interior values are [1.05, -1.4, 2.35]. Use r=0.44. Return the next interior vector.

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


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [6.4, 4.75], "unit": "dimensionless"}

Answer: 6.4

Answer: 4.75

Prompt: A line passes through points (4.5, 33.55) and (4.75, 35.15). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In instrument manual case 283655, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def center_values_006424(values):
    if not values:
        raise ValueError('center_values requires at least one value')
    mean = sum(values) / len(values)
    return [value - mean for value in values]
```
Final: {"answer": "python_code", "function": "center_values_006424"}

Answer: python_code

Prompt: Write a Python function center_values_006424(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.

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

try:
    center_values_006424([])
    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 10.7 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.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 6.3 kg and a = 1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 6.3, "unit": "N"}

Answer: 6.3

Prompt: A cart has mass 6.3 kg and measured acceleration 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 = 6.3 kg and a = 1 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=66 degrees through the sine of 2 theta.
3. Substitute v=79.9 m/s and g=9.81 m/s^2.
Final: {"answer": 483.613, "unit": "m"}

Answer: 483.613

Prompt: A projectile is launched on level ground with no air resistance at speed 79.9 m/s and angle 66 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=66 degrees through the sine of 2 theta.
Substitute v=79.9 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.84 * 8.314 * 263 / 114.3.
Final: {"answer": 73.46, "unit": "kPa"}

Answer: 73.46

Prompt: An ideal gas sample has n=3.84 mol, T=263 K, and V=114.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.84 * 8.314 * 263 / 114.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 760 * 4.385 * 83.
Final: {"answer": 276605.8, "unit": "J"}

Answer: 276605.8

Prompt: A 760 g sample has specific heat 4.385 J/(g*K). How much heat is needed to raise its temperature by 83 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 760 * 4.385 * 83.


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=162.1 V and R=168 ohm.
Final: {"answer": 156.4072, "unit": "W"}

Answer: 156.4072

Prompt: A resistor has resistance 168 ohm and voltage 162.1 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=162.1 V and R=168 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.23 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 401.7479, "unit": "g"}

Answer: 401.7479

Prompt: A sample contains 2.23 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 = 2.23 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2300 mL to 2.3 L.
3. Compute M = 4.115 / 2.3.
Final: {"answer": 1.7891, "unit": "mol/L"}

Answer: 1.7891

Prompt: A solution contains 4.115 mol of solute in 2300 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2300 mL to 2.3 L.
Compute M = 4.115 / 2.3.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 39.351, "unit": "state_units"}

Answer: 39.351

Prompt: Use explicit Euler on dy/dt = -0.47 y with y(0)=73.5, step size h=0.4, for 3 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.
Apply that update for 3 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6.4)=-20.46 and f(-5)=-12.9.
3. The interval width is 1.4.
Final: {"answer": -23.352, "unit": "area_units"}

Answer: -23.352

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5.4x+14.1 from x=-6.4 to x=-5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.4)=-20.46 and f(-5)=-12.9.
The interval width is 1.4.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.38 and add it to the current value.
Final: {"answer": [1.657, 1.316, 0.79], "unit": "temperature_units"}

Answer: 1.657

Answer: 1.316

Answer: 0.79

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=0.75, right=0.3; current interior values are [2.55, 2.0, -0.35]. Use r=0.38. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=33 degrees and keep the unit as newtons.
Final: {"answer": [64.997, 42.2095], "unit": "N"}

Answer: 64.997

Answer: 42.2095

Prompt: A vector has magnitude 77.5 N at 33 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=33 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 simulation spec case 833475, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def center_values_006442(values):
    if not values:
        raise ValueError('center_values requires at least one value')
    mean = sum(values) / len(values)
    return [value - mean for value in values]
```
Final: {"answer": "python_code", "function": "center_values_006442"}

Answer: python_code

Prompt: Write a Python function center_values_006442(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.

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

try:
    center_values_006442([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=2.18 mol and T=244 K, but does not give volume. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 14.65 kg and a = 10.7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 156.755, "unit": "N"}

Answer: 156.755

Prompt: A cart has mass 14.65 kg and measured acceleration 10.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 14.65 kg and a = 10.7 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 25.75^2 and multiply by 0.5 * 15.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5205.0406, "unit": "J"}

Answer: 5205.0406

Prompt: A body of mass 15.7 kg moves at 25.75 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 25.75^2 and multiply by 0.5 * 15.7.
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=63 degrees through the sine of 2 theta.
3. Substitute v=42.2 m/s and g=9.81 m/s^2.
Final: {"answer": 146.8634, "unit": "m"}

Answer: 146.8634

Prompt: A projectile is launched on level ground with no air resistance at speed 42.2 m/s and angle 63 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=63 degrees through the sine of 2 theta.
Substitute v=42.2 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.24 * 8.314 * 285 / 92.3.
Final: {"answer": 57.5044, "unit": "kPa"}

Answer: 57.5044

Prompt: An ideal gas sample has n=2.24 mol, T=285 K, and V=92.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.24 * 8.314 * 285 / 92.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 150 * 4.305 * 32.
Final: {"answer": 20664.0, "unit": "J"}

Answer: 20664.0

Prompt: A 150 g sample has specific heat 4.305 J/(g*K). How much heat is needed to raise its temperature by 32 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 150 * 4.305 * 32.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=142.5 V and R=185.6 ohm.
Final: {"answer": 109.4087, "unit": "W"}

Answer: 109.4087

Prompt: A resistor has resistance 185.6 ohm and voltage 142.5 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=142.5 V and R=185.6 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=17.5 mg, t=132 h, and T_half=93 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 6.5429, "unit": "mg"}

Answer: 6.5429

Prompt: A radioactive sample starts with 17.5 mg. Its half-life is 93 hours. How many mg remain after 132 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=17.5 mg, t=132 h, and T_half=93 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.85 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 125.4285, "unit": "g"}

Answer: 125.4285

Prompt: A sample contains 2.85 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 2.85 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4715 mL to 4.715 L.
3. Compute M = 4.255 / 4.715.
Final: {"answer": 0.9024, "unit": "mol/L"}

Answer: 0.9024

Prompt: A solution contains 4.255 mol of solute in 4715 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4715 mL to 4.715 L.
Compute M = 4.255 / 4.715.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-1)=-23 and f(0.2)=-14.48.
3. The interval width is 1.2.
Final: {"answer": -22.488, "unit": "area_units"}

Answer: -22.488

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.1x+-15.9 from x=-1 to x=0.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-1)=-23 and f(0.2)=-14.48.
The interval width is 1.2.


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=0.16 and add it to the current value.
Final: {"answer": [1.76, -0.098, 1.932], "unit": "temperature_units"}

Answer: 1.76

Answer: -0.098

Answer: 1.932

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=2.9, right=2.7; current interior values are [2.2, -1.25, 2.5]. Use r=0.16. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.16 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 3097.0 / 1000.
Final: {"answer": 3.097, "unit": "kg"}

Answer: 3.097

Prompt: Convert 3097 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 3097.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=72 degrees and keep the unit as newtons.
Final: {"answer": [84.6707, 260.5895], "unit": "N"}

Answer: 84.6707

Answer: 260.5895

Prompt: A vector has magnitude 274 N at 72 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=72 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [1.25, -2.25], "unit": "dimensionless"}

Answer: 1.25

Answer: -2.25

Prompt: A line passes through points (7.75, 7.4375) and (19.25, 21.8125). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In simulation spec case 607251, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def clamp_006460(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_006460"}

Answer: python_code

Prompt: Write a Python function clamp_006460(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.

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

try:
    clamp_006460(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=68.5 and h=0.7, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 43.4^2 and multiply by 0.5 * 0.55.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 517.979, "unit": "J"}

Answer: 517.979

Prompt: A body of mass 0.55 kg moves at 43.4 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 43.4^2 and multiply by 0.5 * 0.55.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.9 * 8.314 * 514 / 83.6.
Final: {"answer": 199.357, "unit": "kPa"}

Answer: 199.357

Prompt: An ideal gas sample has n=3.9 mol, T=514 K, and V=83.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.9 * 8.314 * 514 / 83.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 985 * 3.94 * 4.
Final: {"answer": 15523.6, "unit": "J"}

Answer: 15523.6

Prompt: A 985 g sample has specific heat 3.94 J/(g*K). How much heat is needed to raise its temperature by 4 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 985 * 3.94 * 4.


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=174.4 V and R=147.1 ohm.
Final: {"answer": 206.7666, "unit": "W"}

Answer: 206.7666

Prompt: A resistor has resistance 147.1 ohm and voltage 174.4 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=174.4 V and R=147.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=43.5 mg, t=15 h, and T_half=24 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 28.2063, "unit": "mg"}

Answer: 28.2063

Prompt: A radioactive sample starts with 43.5 mg. Its half-life is 24 hours. How many mg remain after 15 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=43.5 mg, t=15 h, and T_half=24 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.56 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 208.0464, "unit": "g"}

Answer: 208.0464

Prompt: A sample contains 3.56 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 = 3.56 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4310 mL to 4.31 L.
3. Compute M = 4.285 / 4.31.
Final: {"answer": 0.9942, "unit": "mol/L"}

Answer: 0.9942

Prompt: A solution contains 4.285 mol of solute in 4310 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4310 mL to 4.31 L.
Compute M = 4.285 / 4.31.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 0.8837, "unit": "state_units"}

Answer: 0.8837

Prompt: Use explicit Euler on dy/dt = -0.71 y with y(0)=18.5, step size h=0.75, for 4 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(4.1)=-12.05 and f(7.7)=-24.65.
3. The interval width is 3.6.
Final: {"answer": -66.06, "unit": "area_units"}

Answer: -66.06

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.5x+2.3 from x=4.1 to x=7.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.1)=-12.05 and f(7.7)=-24.65.
The interval width is 3.6.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.36 and add it to the current value.
Final: {"answer": [0.428, -0.646, -0.032], "unit": "temperature_units"}

Answer: 0.428

Answer: -0.646

Answer: -0.032

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.95, right=2.15; current interior values are [0.5, -1.15, -1.4]. Use r=0.36. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.36 and add it to the current value.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 225.0 + 273.15.
Final: {"answer": 498.15, "unit": "K"}

Answer: 498.15

Prompt: Convert 225 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 225.0 + 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=18 degrees and keep the unit as newtons.
Final: {"answer": [295.303, 95.9498], "unit": "N"}

Answer: 295.303

Answer: 95.9498

Prompt: A vector has magnitude 310.5 N at 18 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=18 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-8.85, -18.0], "unit": "dimensionless"}

Answer: -8.85

Answer: -18.0

Prompt: A line passes through points (-10.5, 74.925) and (-9.5, 66.075). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In field worksheet case 258430, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def clamp_006478(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_006478"}

Answer: python_code

Prompt: Write a Python function clamp_006478(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.

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

try:
    clamp_006478(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid mobile ledger records in release 281656, 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.