Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 28.8275, "unit": "state_units"}

Answer: 28.8275

Prompt: Use explicit Euler on dy/dt = -0.03 y with y(0)=31, step size h=0.6, 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) = -0.03 y, so each step multiplies y by 1 - h*0.03.
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(-5.1)=-7.11 and f(2.1)=-20.79.
3. The interval width is 7.2.
Final: {"answer": -100.44, "unit": "area_units"}

Answer: -100.44

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.9x+-16.8 from x=-5.1 to x=2.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-5.1)=-7.11 and f(2.1)=-20.79.
The interval width is 7.2.

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


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.3 and add it to the current value.
Final: {"answer": [0.695, 0.285, 0.78], "unit": "temperature_units"}

Answer: 0.695

Answer: 0.285

Answer: 0.78

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.4, right=2.75; current interior values are [-0.25, 2.25, -1.8]. Use r=0.3. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 2201.5 / 100.
Final: {"answer": 22.015, "unit": "m"}

Answer: 22.015

Prompt: Convert 2201.5 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 2201.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=201 degrees and keep the unit as newtons.
Final: {"answer": [-268.4044, -103.0308], "unit": "N"}

Answer: -268.4044

Answer: -103.0308

Prompt: A vector has magnitude 287.5 N at 201 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=201 degrees and keep the unit as newtons.

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


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 model card equation case 716812, 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_003796(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_003796"}

Answer: python_code

Prompt: Write a Python function center_values_003796(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_003796([])
    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)=6 and h=0.85, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 2.75 kg and a = 8.2 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 22.55, "unit": "N"}

Answer: 22.55

Prompt: A cart has mass 2.75 kg and measured acceleration 8.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 2.75 kg and a = 8.2 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 19.6^2 and multiply by 0.5 * 5.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1123.668, "unit": "J"}

Answer: 1123.668

Prompt: A body of mass 5.85 kg moves at 19.6 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 19.6^2 and multiply by 0.5 * 5.85.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=43 degrees through the sine of 2 theta.
3. Substitute v=64.1 m/s and g=9.81 m/s^2.
Final: {"answer": 417.8187, "unit": "m"}

Answer: 417.8187

Prompt: A projectile is launched on level ground with no air resistance at speed 64.1 m/s and angle 43 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=43 degrees through the sine of 2 theta.
Substitute v=64.1 m/s and g=9.81 m/s^2.

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


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1415 * 1.395 * 98.
Final: {"answer": 193444.65, "unit": "J"}

Answer: 193444.65

Prompt: A 1415 g sample has specific heat 1.395 J/(g*K). How much heat is needed to raise its temperature by 98 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1415 * 1.395 * 98.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3540 mL to 3.54 L.
3. Compute M = 4.37 / 3.54.
Final: {"answer": 1.2345, "unit": "mol/L"}

Answer: 1.2345

Prompt: A solution contains 4.37 mol of solute in 3540 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3540 mL to 3.54 L.
Compute M = 4.37 / 3.54.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.23 y, so each step multiplies y by 1 - h*0.23.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 51.4384, "unit": "state_units"}

Answer: 51.4384

Prompt: Use explicit Euler on dy/dt = -0.23 y with y(0)=63.5, step size h=0.15, 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) = -0.23 y, so each step multiplies y by 1 - h*0.23.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.44 and add it to the current value.
Final: {"answer": [1.954, 0.054, 1.618], "unit": "temperature_units"}

Answer: 1.954

Answer: 0.054

Answer: 1.618

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=2.85, right=2.25; current interior values are [0.15, 1.55, -0.45]. Use r=0.44. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1559.0 / 100.
Final: {"answer": 15.59, "unit": "m"}

Answer: 15.59

Prompt: Convert 1559 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 1559.0 / 100.


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

Answer: inconsistent

Prompt: In quality-control check case 555071, 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 safe_mean_003814(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_003814"}

Answer: python_code

Prompt: Write a Python function safe_mean_003814(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_003814([])
    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 laboratory invoice record from batch 895369 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 18.75 kg and a = 10.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 195.9375, "unit": "N"}

Answer: 195.9375

Prompt: A cart has mass 18.75 kg and measured acceleration 10.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 18.75 kg and a = 10.45 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 34.35^2 and multiply by 0.5 * 7.55.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 4454.2074, "unit": "J"}

Answer: 4454.2074

Prompt: A body of mass 7.55 kg moves at 34.35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 34.35^2 and multiply by 0.5 * 7.55.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=20 degrees through the sine of 2 theta.
3. Substitute v=20.6 m/s and g=9.81 m/s^2.
Final: {"answer": 27.8056, "unit": "m"}

Answer: 27.8056

Prompt: A projectile is launched on level ground with no air resistance at speed 20.6 m/s and angle 20 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=20 degrees through the sine of 2 theta.
Substitute v=20.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.31 * 8.314 * 248 / 119.5.
Final: {"answer": 22.6029, "unit": "kPa"}

Answer: 22.6029

Prompt: An ideal gas sample has n=1.31 mol, T=248 K, and V=119.5 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 = 1.31 * 8.314 * 248 / 119.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 440 * 1.995 * 24.
Final: {"answer": 21067.2, "unit": "J"}

Answer: 21067.2

Prompt: A 440 g sample has specific heat 1.995 J/(g*K). How much heat is needed to raise its temperature by 24 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 440 * 1.995 * 24.


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=221.1 V and R=137.5 ohm.
Final: {"answer": 355.5288, "unit": "W"}

Answer: 355.5288

Prompt: A resistor has resistance 137.5 ohm and voltage 221.1 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=221.1 V and R=137.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=426.5 mg, t=260 h, and T_half=78 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 42.3142, "unit": "mg"}

Answer: 42.3142

Prompt: A radioactive sample starts with 426.5 mg. Its half-life is 78 hours. How many mg remain after 260 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=426.5 mg, t=260 h, and T_half=78 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 = 6.18 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 618.5377, "unit": "g"}

Answer: 618.5377

Prompt: A sample contains 6.18 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 = 6.18 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.01 y, so each step multiplies y by 1 - h*0.01.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 9.7177, "unit": "state_units"}

Answer: 9.7177

Prompt: Use explicit Euler on dy/dt = -0.01 y with y(0)=10.5, step size h=1.1, for 7 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.01 y, so each step multiplies y by 1 - h*0.01.
Apply that update for 7 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(5.6)=-30.52 and f(6.1)=-31.62.
3. The interval width is 0.5.
Final: {"answer": -15.535, "unit": "area_units"}

Answer: -15.535

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.2x+-18.2 from x=5.6 to x=6.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(5.6)=-30.52 and f(6.1)=-31.62.
The interval width is 0.5.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.46 and add it to the current value.
Final: {"answer": [-0.758, 1.036, -1.564], "unit": "temperature_units"}

Answer: -0.758

Answer: 1.036

Answer: -1.564

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=0.1, right=-1.6; current interior values are [1.45, -2.0, 1.15]. Use r=0.46. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.46 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 35110.0 / 1000.
Final: {"answer": 35.11, "unit": "kg"}

Answer: 35.11

Prompt: Convert 35110 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 35110.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=318 degrees and keep the unit as newtons.
Final: {"answer": [282.0235, -253.9351], "unit": "N"}

Answer: 282.0235

Answer: -253.9351

Prompt: A vector has magnitude 379.5 N at 318 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=318 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-6.05, -3.0], "unit": "dimensionless"}

Answer: -6.05

Answer: -3.0

Prompt: A line passes through points (-9.5, 54.475) and (0.5, -6.025). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. energy divided by length is force, not spring constant
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In quality-control check case 813950, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
energy divided by length is force, not spring constant
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


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

```python
def clamp_003832(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_003832"}

Answer: python_code

Prompt: Write a Python function clamp_003832(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_003832(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 7.9 kg and a = 9.05 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 71.495, "unit": "N"}

Answer: 71.495

Prompt: A cart has mass 7.9 kg and measured acceleration 9.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 7.9 kg and a = 9.05 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 13^2 and multiply by 0.5 * 25.4.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2146.3, "unit": "J"}

Answer: 2146.3

Prompt: A body of mass 25.4 kg moves at 13 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 13^2 and multiply by 0.5 * 25.4.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=36 degrees through the sine of 2 theta.
3. Substitute v=70.8 m/s and g=9.81 m/s^2.
Final: {"answer": 485.9637, "unit": "m"}

Answer: 485.9637

Prompt: A projectile is launched on level ground with no air resistance at speed 70.8 m/s and angle 36 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=36 degrees through the sine of 2 theta.
Substitute v=70.8 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.22 * 8.314 * 286 / 34.4.
Final: {"answer": 291.6957, "unit": "kPa"}

Answer: 291.6957

Prompt: An ideal gas sample has n=4.22 mol, T=286 K, and V=34.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.22 * 8.314 * 286 / 34.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 330 * 3.025 * 77.
Final: {"answer": 76865.25, "unit": "J"}

Answer: 76865.25

Prompt: A 330 g sample has specific heat 3.025 J/(g*K). How much heat is needed to raise its temperature by 77 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 330 * 3.025 * 77.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=103.5 V and R=53.2 ohm.
Final: {"answer": 201.3581, "unit": "W"}

Answer: 201.3581

Prompt: A resistor has resistance 53.2 ohm and voltage 103.5 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=103.5 V and R=53.2 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=747 mg, t=149 h, and T_half=58 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 125.8882, "unit": "mg"}

Answer: 125.8882

Prompt: A radioactive sample starts with 747 mg. Its half-life is 58 hours. How many mg remain after 149 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=747 mg, t=149 h, and T_half=58 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.82 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 86.8323, "unit": "g"}

Answer: 86.8323

Prompt: A sample contains 4.82 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 = 4.82 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 4385 mL to 4.385 L.
3. Compute M = 3.345 / 4.385.
Final: {"answer": 0.7628, "unit": "mol/L"}

Answer: 0.7628

Prompt: A solution contains 3.345 mol of solute in 4385 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4385 mL to 4.385 L.
Compute M = 3.345 / 4.385.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 8.0037, "unit": "state_units"}

Answer: 8.0037

Prompt: Use explicit Euler on dy/dt = -0.08 y with y(0)=24, step size h=1.3, for 10 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(6.3)=48.71 and f(8.2)=63.34.
3. The interval width is 1.9.
Final: {"answer": 106.4475, "unit": "area_units"}

Answer: 106.4475

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.7x+0.2 from x=6.3 to x=8.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.3)=48.71 and f(8.2)=63.34.
The interval width is 1.9.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.22 and add it to the current value.
Final: {"answer": [1.162, 0.054, 0.722], "unit": "temperature_units"}

Answer: 1.162

Answer: 0.054

Answer: 0.722

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=-0.35, right=0.45; current interior values are [2.9, -1.75, 1.8]. Use r=0.22. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 31482.0 / 1000.
Final: {"answer": 31.482, "unit": "kg"}

Answer: 31.482

Prompt: Convert 31482 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 31482.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=0 degrees and keep the unit as newtons.
Final: {"answer": [422.0, 0.0], "unit": "N"}

Answer: 422.0

Answer: 0.0

Prompt: A vector has magnitude 422 N at 0 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=0 degrees and keep the unit as newtons.


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

```python
def finite_differences_003850(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_003850"}

Answer: python_code

Prompt: Write a Python function finite_differences_003850(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.

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

assert finite_differences_003850([5]) == []

assert finite_differences_003850([]) == []


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 56.3 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 = 24.35 kg and a = 8 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 194.8, "unit": "N"}

Answer: 194.8

Prompt: A cart has mass 24.35 kg and measured acceleration 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 = 24.35 kg and a = 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 = 2.65^2 and multiply by 0.5 * 22.25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 78.1253, "unit": "J"}

Answer: 78.1253

Prompt: A body of mass 22.25 kg moves at 2.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 2.65^2 and multiply by 0.5 * 22.25.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=56 degrees through the sine of 2 theta.
3. Substitute v=83.9 m/s and g=9.81 m/s^2.
Final: {"answer": 665.305, "unit": "m"}

Answer: 665.305

Prompt: A projectile is launched on level ground with no air resistance at speed 83.9 m/s and angle 56 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=56 degrees through the sine of 2 theta.
Substitute v=83.9 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 = 4.11 * 8.314 * 324 / 46.1.
Final: {"answer": 240.1574, "unit": "kPa"}

Answer: 240.1574

Prompt: An ideal gas sample has n=4.11 mol, T=324 K, and V=46.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.11 * 8.314 * 324 / 46.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 35 * 3.005 * 97.
Final: {"answer": 10201.975, "unit": "J"}

Answer: 10201.975

Prompt: A 35 g sample has specific heat 3.005 J/(g*K). How much heat is needed to raise its temperature by 97 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 35 * 3.005 * 97.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=18.2 V and R=157 ohm.
Final: {"answer": 2.1098, "unit": "W"}

Answer: 2.1098

Prompt: A resistor has resistance 157 ohm and voltage 18.2 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=18.2 V and R=157 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=138 mg, t=117.5 h, and T_half=20.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 2.5969, "unit": "mg"}

Answer: 2.5969

Prompt: A radioactive sample starts with 138 mg. Its half-life is 20.5 hours. How many mg remain after 117.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=138 mg, t=117.5 h, and T_half=20.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.1 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 378.3276, "unit": "g"}

Answer: 378.3276

Prompt: A sample contains 2.1 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 = 2.1 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 3865 mL to 3.865 L.
3. Compute M = 2.21 / 3.865.
Final: {"answer": 0.5718, "unit": "mol/L"}

Answer: 0.5718

Prompt: A solution contains 2.21 mol of solute in 3865 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3865 mL to 3.865 L.
Compute M = 2.21 / 3.865.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-9)=-40.2 and f(-7.5)=-33.15.
3. The interval width is 1.5.
Final: {"answer": -55.0125, "unit": "area_units"}

Answer: -55.0125

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.7x+2.1 from x=-9 to x=-7.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9)=-40.2 and f(-7.5)=-33.15.
The interval width is 1.5.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.06 and add it to the current value.
Final: {"answer": [0.356, 1.959, 1.503], "unit": "temperature_units"}

Answer: 0.356

Answer: 1.959

Answer: 1.503

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.9, right=-1.25; current interior values are [0.2, 2.1, 1.65]. Use r=0.06. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 23.0 + 273.15.
Final: {"answer": 296.15, "unit": "K"}

Answer: 296.15

Prompt: Convert 23 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 23.0 + 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=81 degrees and keep the unit as newtons.
Final: {"answer": [30.1919, 190.6238], "unit": "N"}

Answer: 30.1919

Answer: 190.6238

Prompt: A vector has magnitude 193 N at 81 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=81 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": [-1.0, -27.0], "unit": "dimensionless"}

Answer: -1.0

Answer: -27.0

Prompt: A line passes through points (-17, -10) and (-13.5, -13.5). Return [slope, intercept] for y = slope*x + intercept.

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


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

```python
def finite_differences_003868(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_003868"}

Answer: python_code

Prompt: Write a Python function finite_differences_003868(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.

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

assert finite_differences_003868([5]) == []

assert finite_differences_003868([]) == []


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 crop records in release 448901, 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 = 17.25 kg and a = 11.05 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 190.6125, "unit": "N"}

Answer: 190.6125

Prompt: A cart has mass 17.25 kg and measured acceleration 11.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 17.25 kg and a = 11.05 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=10 degrees through the sine of 2 theta.
3. Substitute v=34.8 m/s and g=9.81 m/s^2.
Final: {"answer": 42.2222, "unit": "m"}

Answer: 42.2222

Prompt: A projectile is launched on level ground with no air resistance at speed 34.8 m/s and angle 10 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=10 degrees through the sine of 2 theta.
Substitute v=34.8 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 = 0.13 * 8.314 * 382 / 12.7.
Final: {"answer": 32.5097, "unit": "kPa"}

Answer: 32.5097

Prompt: An ideal gas sample has n=0.13 mol, T=382 K, and V=12.7 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 = 0.13 * 8.314 * 382 / 12.7.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=135 mg, t=1.5 h, and T_half=40 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 131.5362, "unit": "mg"}

Answer: 131.5362

Prompt: A radioactive sample starts with 135 mg. Its half-life is 40 hours. How many mg remain after 1.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=135 mg, t=1.5 h, and T_half=40 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 = 7.58 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 758.6595, "unit": "g"}

Answer: 758.6595

Prompt: A sample contains 7.58 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.58 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 500 mL to 0.5 L.
3. Compute M = 0.64 / 0.5.
Final: {"answer": 1.28, "unit": "mol/L"}

Answer: 1.28

Prompt: A solution contains 0.64 mol of solute in 500 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 500 mL to 0.5 L.
Compute M = 0.64 / 0.5.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.52 y, so each step multiplies y by 1 - h*0.52.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.52 y with y(0)=55, step size h=1.95, 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) = -0.52 y, so each step multiplies y by 1 - h*0.52.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(7)=-31.3 and f(13)=-47.5.
3. The interval width is 6.
Final: {"answer": -236.4, "unit": "area_units"}

Answer: -236.4

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.7x+-12.4 from x=7 to x=13. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7)=-31.3 and f(13)=-47.5.
The interval width is 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=0.04 and add it to the current value.
Final: {"answer": [0.134, 2.002, 2.804], "unit": "temperature_units"}

Answer: 0.134

Answer: 2.002

Answer: 2.804

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.3, right=1.35; current interior values are [0.0, 2.05, 2.9]. 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 56.5 + 273.15.
Final: {"answer": 329.65, "unit": "K"}

Answer: 329.65

Prompt: Convert 56.5 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 56.5 + 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=319 degrees and keep the unit as newtons.
Final: {"answer": [342.2608, -297.5228], "unit": "N"}

Answer: 342.2608

Answer: -297.5228

Prompt: A vector has magnitude 453.5 N at 319 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=319 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": [-1.75, 5.0], "unit": "dimensionless"}

Answer: -1.75

Answer: 5.0

Prompt: A line passes through points (-4.5, 12.875) and (-1, 6.75). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In student derivation case 616650, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def pairwise_ratios_003886(numerators, denominators):
    if len(numerators) != len(denominators):
        raise ValueError('length mismatch')
    out = []
    for numerator, denominator in zip(numerators, denominators):
        if denominator == 0:
            raise ValueError('zero denominator')
        out.append(numerator / denominator)
    return out
```
Final: {"answer": "python_code", "function": "pairwise_ratios_003886"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_003886(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator 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.

try:
    pairwise_ratios_003886([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_003886([1, 2], [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: 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 allocation scoring problem with 599 items and budget 44210, 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 = 15.4^2 and multiply by 0.5 * 25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2964.5, "unit": "J"}

Answer: 2964.5

Prompt: A body of mass 25 kg moves at 15.4 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 15.4^2 and multiply by 0.5 * 25.
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 = 5.16 * 8.314 * 550 / 46.6.
Final: {"answer": 506.3333, "unit": "kPa"}

Answer: 506.3333

Prompt: An ideal gas sample has n=5.16 mol, T=550 K, and V=46.6 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 = 5.16 * 8.314 * 550 / 46.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1315 * 2.825 * 100.
Final: {"answer": 371487.5, "unit": "J"}

Answer: 371487.5

Prompt: A 1315 g sample has specific heat 2.825 J/(g*K). How much heat is needed to raise its temperature by 100 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1315 * 2.825 * 100.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=216.9 V and R=125.1 ohm.
Final: {"answer": 376.064, "unit": "W"}

Answer: 376.064

Prompt: A resistor has resistance 125.1 ohm and voltage 216.9 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=216.9 V and R=125.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=347 mg, t=103 h, and T_half=54.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 93.629, "unit": "mg"}

Answer: 93.629

Prompt: A radioactive sample starts with 347 mg. Its half-life is 54.5 hours. How many mg remain after 103 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=347 mg, t=103 h, and T_half=54.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.01 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 44.4501, "unit": "g"}

Answer: 44.4501

Prompt: A sample contains 1.01 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.01 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 2005 mL to 2.005 L.
3. Compute M = 1.225 / 2.005.
Final: {"answer": 0.611, "unit": "mol/L"}

Answer: 0.611

Prompt: A solution contains 1.225 mol of solute in 2005 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2005 mL to 2.005 L.
Compute M = 1.225 / 2.005.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.83 y, so each step multiplies y by 1 - h*0.83.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 0.3241, "unit": "state_units"}

Answer: 0.3241

Prompt: Use explicit Euler on dy/dt = -0.83 y with y(0)=28, step size h=1.6, 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) = -0.83 y, so each step multiplies y by 1 - h*0.83.
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(3)=-20.3 and f(12.3)=-74.24.
3. The interval width is 9.3.
Final: {"answer": -439.611, "unit": "area_units"}

Answer: -439.611

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.8x+-2.9 from x=3 to x=12.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3)=-20.3 and f(12.3)=-74.24.
The interval width is 9.3.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.28 and add it to the current value.
Final: {"answer": [0.808, 1.886, 2.314], "unit": "temperature_units"}

Answer: 0.808

Answer: 1.886

Answer: 2.314

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.85, right=2.8; current interior values are [0.5, 2.95, 1.6]. Use r=0.28. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.28 and add it to the current value.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 8.0 + 273.15.
Final: {"answer": 281.15, "unit": "K"}

Answer: 281.15

Prompt: Convert 8 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 8.0 + 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=64 degrees and keep the unit as newtons.
Final: {"answer": [0.8767, 1.7976], "unit": "N"}

Answer: 0.8767

Answer: 1.7976

Prompt: A vector has magnitude 2 N at 64 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=64 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [2.6, -17.5], "unit": "dimensionless"}

Answer: 2.6

Answer: -17.5

Prompt: A line passes through points (9.75, 7.85) and (23.5, 43.6). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. speed squared over acceleration has units of meters
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In lab notebook case 888889, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def pairwise_ratios_003904(numerators, denominators):
    if len(numerators) != len(denominators):
        raise ValueError('length mismatch')
    out = []
    for numerator, denominator in zip(numerators, denominators):
        if denominator == 0:
            raise ValueError('zero denominator')
        out.append(numerator / denominator)
    return out
```
Final: {"answer": "python_code", "function": "pairwise_ratios_003904"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_003904(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator 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.

try:
    pairwise_ratios_003904([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_003904([1, 2], [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: volume.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=0.7 mol and T=344 K, but does not give volume. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 12.55^2 and multiply by 0.5 * 9.1.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 716.6364, "unit": "J"}

Answer: 716.6364

Prompt: A body of mass 9.1 kg moves at 12.55 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 12.55^2 and multiply by 0.5 * 9.1.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=44 degrees through the sine of 2 theta.
3. Substitute v=50.2 m/s and g=9.81 m/s^2.
Final: {"answer": 256.7283, "unit": "m"}

Answer: 256.7283

Prompt: A projectile is launched on level ground with no air resistance at speed 50.2 m/s and angle 44 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=44 degrees through the sine of 2 theta.
Substitute v=50.2 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.6 * 8.314 * 322 / 115.5.
Final: {"answer": 83.4423, "unit": "kPa"}

Answer: 83.4423

Prompt: An ideal gas sample has n=3.6 mol, T=322 K, and V=115.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.6 * 8.314 * 322 / 115.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 230 * 4.18 * 60.
Final: {"answer": 57684.0, "unit": "J"}

Answer: 57684.0

Prompt: A 230 g sample has specific heat 4.18 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 = 230 * 4.18 * 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=239.1 V and R=31.8 ohm.
Final: {"answer": 1797.7613, "unit": "W"}

Answer: 1797.7613

Prompt: A resistor has resistance 31.8 ohm and voltage 239.1 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=239.1 V and R=31.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=971 mg, t=257 h, and T_half=26.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 1.169, "unit": "mg"}

Answer: 1.169

Prompt: A radioactive sample starts with 971 mg. Its half-life is 26.5 hours. How many mg remain after 257 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=971 mg, t=257 h, and T_half=26.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.41 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 282.1041, "unit": "g"}

Answer: 282.1041

Prompt: A sample contains 6.41 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 = 6.41 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 3465 mL to 3.465 L.
3. Compute M = 3.095 / 3.465.
Final: {"answer": 0.8932, "unit": "mol/L"}

Answer: 0.8932

Prompt: A solution contains 3.095 mol of solute in 3465 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3465 mL to 3.465 L.
Compute M = 3.095 / 3.465.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(0.8)=-2.86 and f(9.1)=-8.67.
3. The interval width is 8.3.
Final: {"answer": -47.8495, "unit": "area_units"}

Answer: -47.8495

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.7x+-2.3 from x=0.8 to x=9.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(0.8)=-2.86 and f(9.1)=-8.67.
The interval width is 8.3.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.4 and add it to the current value.
Final: {"answer": [-1.0, -0.78, 0.36], "unit": "temperature_units"}

Answer: -1.0

Answer: -0.78

Answer: 0.36

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=-0.55, right=2.2; current interior values are [-1.3, -1.3, 0.0]. Use r=0.4. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=205 degrees and keep the unit as newtons.
Final: {"answer": [-64.801, -30.2172], "unit": "N"}

Answer: -64.801

Answer: -30.2172

Prompt: A vector has magnitude 71.5 N at 205 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=205 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. energy divided by length is force, not spring constant
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In sensor calibration case 231839, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
energy divided by length is force, not spring constant
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


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

```python
def center_values_003922(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_003922"}

Answer: python_code

Prompt: Write a Python function center_values_003922(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_003922([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.02 and interior values [1.3, -0.2, 1.3], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 7.85 kg and a = 2.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 22.3725, "unit": "N"}

Answer: 22.3725

Prompt: A cart has mass 7.85 kg and measured acceleration 2.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 7.85 kg and a = 2.85 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 0.65^2 and multiply by 0.5 * 12.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2.5984, "unit": "J"}

Answer: 2.5984

Prompt: A body of mass 12.3 kg moves at 0.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 0.65^2 and multiply by 0.5 * 12.3.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=56 degrees through the sine of 2 theta.
3. Substitute v=45.8 m/s and g=9.81 m/s^2.
Final: {"answer": 198.2567, "unit": "m"}

Answer: 198.2567

Prompt: A projectile is launched on level ground with no air resistance at speed 45.8 m/s and angle 56 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=56 degrees through the sine of 2 theta.
Substitute v=45.8 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 = 0.62 * 8.314 * 587 / 30.4.
Final: {"answer": 99.5328, "unit": "kPa"}

Answer: 99.5328

Prompt: An ideal gas sample has n=0.62 mol, T=587 K, and V=30.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.62 * 8.314 * 587 / 30.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 720 * 4.39 * 23.
Final: {"answer": 72698.4, "unit": "J"}

Answer: 72698.4

Prompt: A 720 g sample has specific heat 4.39 J/(g*K). How much heat is needed to raise its temperature by 23 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 720 * 4.39 * 23.


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=153.5 V and R=53.9 ohm.
Final: {"answer": 437.1475, "unit": "W"}

Answer: 437.1475

Prompt: A resistor has resistance 53.9 ohm and voltage 153.5 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=153.5 V and R=53.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=398.5 mg, t=236 h, and T_half=2.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0, "unit": "mg"}

Answer: 0.0

Prompt: A radioactive sample starts with 398.5 mg. Its half-life is 2.5 hours. How many mg remain after 236 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=398.5 mg, t=236 h, and T_half=2.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2825 mL to 2.825 L.
3. Compute M = 0.78 / 2.825.
Final: {"answer": 0.2761, "unit": "mol/L"}

Answer: 0.2761

Prompt: A solution contains 0.78 mol of solute in 2825 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2825 mL to 2.825 L.
Compute M = 0.78 / 2.825.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.2009, "unit": "state_units"}

Answer: 0.2009

Prompt: Use explicit Euler on dy/dt = -0.21 y with y(0)=73.5, step size h=1.85, for 12 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.
Apply that update for 12 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(3.2)=26.26 and f(6.2)=40.66.
3. The interval width is 3.
Final: {"answer": 100.38, "unit": "area_units"}

Answer: 100.38

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.8x+10.9 from x=3.2 to x=6.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3.2)=26.26 and f(6.2)=40.66.
The interval width is 3.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.26 and add it to the current value.
Final: {"answer": [-0.864, 0.198, 1.0], "unit": "temperature_units"}

Answer: -0.864

Answer: 0.198

Answer: 1.0

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.55, right=2.85; current interior values are [-1.8, 1.55, -0.3]. Use r=0.26. 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=0.26 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 2589.0 / 100.
Final: {"answer": 25.89, "unit": "m"}

Answer: 25.89

Prompt: Convert 2589 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 2589.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=262 degrees and keep the unit as newtons.
Final: {"answer": [-58.731, -417.8931], "unit": "N"}

Answer: -58.731

Answer: -417.8931

Prompt: A vector has magnitude 422 N at 262 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=262 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-6.5, 19.0], "unit": "dimensionless"}

Answer: -6.5

Answer: 19.0

Prompt: A line passes through points (15.75, -83.375) and (30.25, -177.625). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In quality-control check case 646506, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def clamp_003940(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_003940"}

Answer: python_code

Prompt: Write a Python function clamp_003940(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_003940(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 13.75 kg and a = 3.15 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 43.3125, "unit": "N"}

Answer: 43.3125

Prompt: A cart has mass 13.75 kg and measured acceleration 3.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 13.75 kg and a = 3.15 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 34.4^2 and multiply by 0.5 * 18.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 11123.584, "unit": "J"}

Answer: 11123.584

Prompt: A body of mass 18.8 kg moves at 34.4 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 34.4^2 and multiply by 0.5 * 18.8.
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=12 degrees through the sine of 2 theta.
3. Substitute v=54.5 m/s and g=9.81 m/s^2.
Final: {"answer": 123.1508, "unit": "m"}

Answer: 123.1508

Prompt: A projectile is launched on level ground with no air resistance at speed 54.5 m/s and angle 12 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=12 degrees through the sine of 2 theta.
Substitute v=54.5 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.07 * 8.314 * 535 / 115.8.
Final: {"answer": 41.0997, "unit": "kPa"}

Answer: 41.0997

Prompt: An ideal gas sample has n=1.07 mol, T=535 K, and V=115.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.07 * 8.314 * 535 / 115.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 75 * 4.415 * 51.
Final: {"answer": 16887.375, "unit": "J"}

Answer: 16887.375

Prompt: A 75 g sample has specific heat 4.415 J/(g*K). How much heat is needed to raise its temperature by 51 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 75 * 4.415 * 51.


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=57.9 V and R=152.7 ohm.
Final: {"answer": 21.9542, "unit": "W"}

Answer: 21.9542

Prompt: A resistor has resistance 152.7 ohm and voltage 57.9 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=57.9 V and R=152.7 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.76 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 278.1744, "unit": "g"}

Answer: 278.1744

Prompt: A sample contains 4.76 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 = 4.76 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 3395 mL to 3.395 L.
3. Compute M = 1.925 / 3.395.
Final: {"answer": 0.567, "unit": "mol/L"}

Answer: 0.567

Prompt: A solution contains 1.925 mol of solute in 3395 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3395 mL to 3.395 L.
Compute M = 1.925 / 3.395.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.8 y, so each step multiplies y by 1 - h*0.8.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": -0.0015, "unit": "state_units"}

Answer: -0.0015

Prompt: Use explicit Euler on dy/dt = -0.8 y with y(0)=23.5, step size h=1.3, 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) = -0.8 y, so each step multiplies y by 1 - h*0.8.
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(6.6)=12.32 and f(8.4)=20.78.
3. The interval width is 1.8.
Final: {"answer": 29.79, "unit": "area_units"}

Answer: 29.79

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.7x+-18.7 from x=6.6 to x=8.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.6)=12.32 and f(8.4)=20.78.
The interval width is 1.8.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.32 and add it to the current value.
Final: {"answer": [-0.472, -0.38, -0.5], "unit": "temperature_units"}

Answer: -0.472

Answer: -0.38

Answer: -0.5

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.25, right=-0.85; current interior values are [-0.2, -1.5, 0.7]. Use r=0.32. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 12791.0 / 1000.
Final: {"answer": 12.791, "unit": "kg"}

Answer: 12.791

Prompt: Convert 12791 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 12791.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=172 degrees and keep the unit as newtons.
Final: {"answer": [-411.4564, 57.8264], "unit": "N"}

Answer: -411.4564

Answer: 57.8264

Prompt: A vector has magnitude 415.5 N at 172 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=172 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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)=17.5 and h=0.8, 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. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=37 degrees through the sine of 2 theta.
3. Substitute v=42.2 m/s and g=9.81 m/s^2.
Final: {"answer": 174.5008, "unit": "m"}

Answer: 174.5008

Prompt: A projectile is launched on level ground with no air resistance at speed 42.2 m/s and angle 37 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=37 degrees through the sine of 2 theta.
Substitute v=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 = 4.5 * 8.314 * 545 / 112.5.
Final: {"answer": 181.2452, "unit": "kPa"}

Answer: 181.2452

Prompt: An ideal gas sample has n=4.5 mol, T=545 K, and V=112.5 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 = 4.5 * 8.314 * 545 / 112.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1145 * 3.105 * 41.
Final: {"answer": 145764.225, "unit": "J"}

Answer: 145764.225

Prompt: A 1145 g sample has specific heat 3.105 J/(g*K). How much heat is needed to raise its temperature by 41 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1145 * 3.105 * 41.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=121.5 V and R=190 ohm.
Final: {"answer": 77.6961, "unit": "W"}

Answer: 77.6961

Prompt: A resistor has resistance 190 ohm and voltage 121.5 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=121.5 V and R=190 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=155.5 mg, t=302.5 h, and T_half=58.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 4.3164, "unit": "mg"}

Answer: 4.3164

Prompt: A radioactive sample starts with 155.5 mg. Its half-life is 58.5 hours. How many mg remain after 302.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=155.5 mg, t=302.5 h, and T_half=58.5 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 = 5.47 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 319.6668, "unit": "g"}

Answer: 319.6668

Prompt: A sample contains 5.47 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.47 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 4410 mL to 4.41 L.
3. Compute M = 1.315 / 4.41.
Final: {"answer": 0.2982, "unit": "mol/L"}

Answer: 0.2982

Prompt: A solution contains 1.315 mol of solute in 4410 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4410 mL to 4.41 L.
Compute M = 1.315 / 4.41.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.89 y, so each step multiplies y by 1 - h*0.89.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": -0.0013, "unit": "state_units"}

Answer: -0.0013

Prompt: Use explicit Euler on dy/dt = -0.89 y with y(0)=72, step size h=1.25, 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) = -0.89 y, so each step multiplies y by 1 - h*0.89.
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(1.4)=-16.76 and f(10.6)=-61.84.
3. The interval width is 9.2.
Final: {"answer": -361.56, "unit": "area_units"}

Answer: -361.56

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.9x+-9.9 from x=1.4 to x=10.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.4)=-16.76 and f(10.6)=-61.84.
The interval width is 9.2.


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=0.14 and add it to the current value.
Final: {"answer": [0.516, 2.059, 0.759], "unit": "temperature_units"}

Answer: 0.516

Answer: 2.059

Answer: 0.759

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=1.8; current interior values are [-0.1, 2.85, 0.15]. Use r=0.14. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.14 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 42565.0 / 1000.
Final: {"answer": 42.565, "unit": "kg"}

Answer: 42.565

Prompt: Convert 42565 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 42565.0 / 1000.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [3.6, 20.5], "unit": "dimensionless"}

Answer: 3.6

Answer: 20.5

Prompt: A line passes through points (-0.5, 18.7) and (6.5, 43.9). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In sensor calibration case 875320, 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_003976(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_003976"}

Answer: python_code

Prompt: Write a Python function clamp_003976(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_003976(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: recurrence, objective, tie_breaking_rule.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a segmentation scoring problem with 1215 items and budget 95770, 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 = 11.45^2 and multiply by 0.5 * 6.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 445.7485, "unit": "J"}

Answer: 445.7485

Prompt: A body of mass 6.8 kg moves at 11.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 11.45^2 and multiply by 0.5 * 6.8.
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=32 degrees through the sine of 2 theta.
3. Substitute v=75.1 m/s and g=9.81 m/s^2.
Final: {"answer": 516.7388, "unit": "m"}

Answer: 516.7388

Prompt: A projectile is launched on level ground with no air resistance at speed 75.1 m/s and angle 32 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=32 degrees through the sine of 2 theta.
Substitute v=75.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.37 * 8.314 * 503 / 38.4.
Final: {"answer": 367.009, "unit": "kPa"}

Answer: 367.009

Prompt: An ideal gas sample has n=3.37 mol, T=503 K, and V=38.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.37 * 8.314 * 503 / 38.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1115 * 3.13 * 76.
Final: {"answer": 265236.2, "unit": "J"}

Answer: 265236.2

Prompt: A 1115 g sample has specific heat 3.13 J/(g*K). How much heat is needed to raise its temperature by 76 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1115 * 3.13 * 76.


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=27.2 V and R=87.3 ohm.
Final: {"answer": 8.4747, "unit": "W"}

Answer: 8.4747

Prompt: A resistor has resistance 87.3 ohm and voltage 27.2 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=27.2 V and R=87.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=115.5 mg, t=255 h, and T_half=92 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 16.9124, "unit": "mg"}

Answer: 16.9124

Prompt: A radioactive sample starts with 115.5 mg. Its half-life is 92 hours. How many mg remain after 255 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=115.5 mg, t=255 h, and T_half=92 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.06 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 190.9654, "unit": "g"}

Answer: 190.9654

Prompt: A sample contains 1.06 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.06 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 4825 mL to 4.825 L.
3. Compute M = 0.175 / 4.825.
Final: {"answer": 0.0363, "unit": "mol/L"}

Answer: 0.0363

Prompt: A solution contains 0.175 mol of solute in 4825 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4825 mL to 4.825 L.
Compute M = 0.175 / 4.825.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.92 y, so each step multiplies y by 1 - h*0.92.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": -2.5111, "unit": "state_units"}

Answer: -2.5111

Prompt: Use explicit Euler on dy/dt = -0.92 y with y(0)=6, step size h=1.9, 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) = -0.92 y, so each step multiplies y by 1 - h*0.92.
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(1.6)=-20.96 and f(7)=-32.3.
3. The interval width is 5.4.
Final: {"answer": -143.802, "unit": "area_units"}

Answer: -143.802

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.1x+-17.6 from x=1.6 to x=7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.6)=-20.96 and f(7)=-32.3.
The interval width is 5.4.


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=0.04 and add it to the current value.
Final: {"answer": [-0.956, 0.878, -0.93], "unit": "temperature_units"}

Answer: -0.956

Answer: 0.878

Answer: -0.93

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=-0.8, right=2.15; current interior values are [-1.05, 1.05, -1.15]. Use r=0.04. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 2601.5 / 100.
Final: {"answer": 26.015, "unit": "m"}

Answer: 26.015

Prompt: Convert 2601.5 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 2601.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=7 degrees and keep the unit as newtons.
Final: {"answer": [251.6104, 30.8939], "unit": "N"}

Answer: 251.6104

Answer: 30.8939

Prompt: A vector has magnitude 253.5 N at 7 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

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


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

Answer: consistent

Prompt: In lab notebook case 296503, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def weighted_sum_003994(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_003994"}

Answer: python_code

Prompt: Write a Python function weighted_sum_003994(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

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

try:
    weighted_sum_003994([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 field sensor records in release 992062, 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 = 6.75 kg and a = 7.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 52.9875, "unit": "N"}

Answer: 52.9875

Prompt: A cart has mass 6.75 kg and measured acceleration 7.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 6.75 kg and a = 7.85 m/s^2.
The unit kg*m/s^2 is one newton.