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=0.48 and interior values [-0.1, -0.05, 0.05], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 19.85 kg and a = 7.8 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 154.83, "unit": "N"}

Answer: 154.83

Prompt: A cart has mass 19.85 kg and measured acceleration 7.8 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 = 19.85 kg and a = 7.8 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 = 32.35^2 and multiply by 0.5 * 15.1.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 7901.2449, "unit": "J"}

Answer: 7901.2449

Prompt: A body of mass 15.1 kg moves at 32.35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 32.35^2 and multiply by 0.5 * 15.1.
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=72 degrees through the sine of 2 theta.
3. Substitute v=13.7 m/s and g=9.81 m/s^2.
Final: {"answer": 11.2458, "unit": "m"}

Answer: 11.2458

Prompt: A projectile is launched on level ground with no air resistance at speed 13.7 m/s and angle 72 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=72 degrees through the sine of 2 theta.
Substitute v=13.7 m/s and g=9.81 m/s^2.

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


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.01 * 8.314 * 506 / 17.1.
Final: {"answer": 986.5266, "unit": "kPa"}

Answer: 986.5266

Prompt: An ideal gas sample has n=4.01 mol, T=506 K, and V=17.1 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 = 4.01 * 8.314 * 506 / 17.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1725 * 3.8 * 4.
Final: {"answer": 26220.0, "unit": "J"}

Answer: 26220.0

Prompt: A 1725 g sample has specific heat 3.8 J/(g*K). How much heat is needed to raise its temperature by 4 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1725 * 3.8 * 4.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=269 mg, t=57.5 h, and T_half=102 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 181.9927, "unit": "mg"}

Answer: 181.9927

Prompt: A radioactive sample starts with 269 mg. Its half-life is 102 hours. How many mg remain after 57.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=269 mg, t=57.5 h, and T_half=102 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.43 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 143.1244, "unit": "g"}

Answer: 143.1244

Prompt: A sample contains 1.43 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.43 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 1450 mL to 1.45 L.
3. Compute M = 1.425 / 1.45.
Final: {"answer": 0.9828, "unit": "mol/L"}

Answer: 0.9828

Prompt: A solution contains 1.425 mol of solute in 1450 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1450 mL to 1.45 L.
Compute M = 1.425 / 1.45.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.57 y, so each step multiplies y by 1 - h*0.57.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.57 y with y(0)=13, step size h=1.9, for 11 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.57 y, so each step multiplies y by 1 - h*0.57.
Apply that update for 11 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(1.7)=-18.8 and f(2.1)=-20.
3. The interval width is 0.4.
Final: {"answer": -7.76, "unit": "area_units"}

Answer: -7.76

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-3x+-13.7 from x=1.7 to x=2.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.7)=-18.8 and f(2.1)=-20.
The interval width is 0.4.

(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=0.22 and add it to the current value.
Final: {"answer": [-0.758, -0.9, -0.396], "unit": "temperature_units"}

Answer: -0.758

Answer: -0.9

Answer: -0.396

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=2.75; current interior values are [-1.55, -0.35, -1.65]. 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. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [5.15, -22.25], "unit": "dimensionless"}

Answer: 5.15

Answer: -22.25

Prompt: A line passes through points (-3.5, -40.275) and (9.25, 25.3875). 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 student derivation case 390731, 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. 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)=27 and h=1.3, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 4.2 kg and a = 4.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 18.9, "unit": "N"}

Answer: 18.9

Prompt: A cart has mass 4.2 kg and measured acceleration 4.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 4.2 kg and a = 4.5 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=55 degrees through the sine of 2 theta.
3. Substitute v=49 m/s and g=9.81 m/s^2.
Final: {"answer": 229.99, "unit": "m"}

Answer: 229.99

Prompt: A projectile is launched on level ground with no air resistance at speed 49 m/s and angle 55 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=55 degrees through the sine of 2 theta.
Substitute v=49 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 = 0.31 * 8.314 * 391 / 38.7.
Final: {"answer": 26.0398, "unit": "kPa"}

Answer: 26.0398

Prompt: An ideal gas sample has n=0.31 mol, T=391 K, and V=38.7 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 = 0.31 * 8.314 * 391 / 38.7.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=191 mg, t=206 h, and T_half=45.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 8.2819, "unit": "mg"}

Answer: 8.2819

Prompt: A radioactive sample starts with 191 mg. Its half-life is 45.5 hours. How many mg remain after 206 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=191 mg, t=206 h, and T_half=45.5 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 985 mL to 0.985 L.
3. Compute M = 3.88 / 0.985.
Final: {"answer": 3.9391, "unit": "mol/L"}

Answer: 3.9391

Prompt: A solution contains 3.88 mol of solute in 985 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 985 mL to 0.985 L.
Compute M = 3.88 / 0.985.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.19 y, so each step multiplies y by 1 - h*0.19.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 6.8787, "unit": "state_units"}

Answer: 6.8787

Prompt: Use explicit Euler on dy/dt = -0.19 y with y(0)=35, step size h=1.25, 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) = -0.19 y, so each step multiplies y by 1 - h*0.19.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(5.9)=-10.86 and f(14.7)=-31.98.
3. The interval width is 8.8.
Final: {"answer": -188.496, "unit": "area_units"}

Answer: -188.496

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.4x+3.3 from x=5.9 to x=14.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(5.9)=-10.86 and f(14.7)=-31.98.
The interval width is 8.8.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=178 degrees and keep the unit as newtons.
Final: {"answer": [-272.8337, 9.5276], "unit": "N"}

Answer: -272.8337

Answer: 9.5276

Prompt: A vector has magnitude 273 N at 178 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=178 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. 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 model card equation case 213457, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def center_values_005380(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_005380"}

Answer: python_code

Prompt: Write a Python function center_values_005380(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_005380([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 9.8 kg and a = 3.9 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 38.22, "unit": "N"}

Answer: 38.22

Prompt: A cart has mass 9.8 kg and measured acceleration 3.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 9.8 kg and a = 3.9 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=77 degrees through the sine of 2 theta.
3. Substitute v=41.4 m/s and g=9.81 m/s^2.
Final: {"answer": 76.5903, "unit": "m"}

Answer: 76.5903

Prompt: A projectile is launched on level ground with no air resistance at speed 41.4 m/s and angle 77 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=77 degrees through the sine of 2 theta.
Substitute v=41.4 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 = 1.03 * 8.314 * 334 / 89.9.
Final: {"answer": 31.8152, "unit": "kPa"}

Answer: 31.8152

Prompt: An ideal gas sample has n=1.03 mol, T=334 K, and V=89.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.03 * 8.314 * 334 / 89.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1280 * 3.92 * 34.
Final: {"answer": 170598.4, "unit": "J"}

Answer: 170598.4

Prompt: A 1280 g sample has specific heat 3.92 J/(g*K). How much heat is needed to raise its temperature by 34 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1280 * 3.92 * 34.


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=74.8 V and R=178.2 ohm.
Final: {"answer": 31.3975, "unit": "W"}

Answer: 31.3975

Prompt: A resistor has resistance 178.2 ohm and voltage 74.8 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=74.8 V and R=178.2 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=634.5 mg, t=307 h, and T_half=40.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 3.3155, "unit": "mg"}

Answer: 3.3155

Prompt: A radioactive sample starts with 634.5 mg. Its half-life is 40.5 hours. How many mg remain after 307 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=634.5 mg, t=307 h, and T_half=40.5 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 = 2.69 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 269.234, "unit": "g"}

Answer: 269.234

Prompt: A sample contains 2.69 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 = 2.69 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 4480 mL to 4.48 L.
3. Compute M = 0.885 / 4.48.
Final: {"answer": 0.1975, "unit": "mol/L"}

Answer: 0.1975

Prompt: A solution contains 0.885 mol of solute in 4480 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4480 mL to 4.48 L.
Compute M = 0.885 / 4.48.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(3.6)=-9.7 and f(4.9)=-11.65.
3. The interval width is 1.3.
Final: {"answer": -13.8775, "unit": "area_units"}

Answer: -13.8775

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.5x+-4.3 from x=3.6 to x=4.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3.6)=-9.7 and f(4.9)=-11.65.
The interval width is 1.3.


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=0.22 and add it to the current value.
Final: {"answer": [0.843, 1.018, 0.216], "unit": "temperature_units"}

Answer: 0.843

Answer: 1.018

Answer: 0.216

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=1.75, right=-1.1; current interior values are [0.15, 1.7, 0.15]. 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 38020.0 / 1000.
Final: {"answer": 38.02, "unit": "kg"}

Answer: 38.02

Prompt: Convert 38020 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 38020.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=39 degrees and keep the unit as newtons.
Final: {"answer": [190.0122, 153.8688], "unit": "N"}

Answer: 190.0122

Answer: 153.8688

Prompt: A vector has magnitude 244.5 N at 39 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=39 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": [1.4, -2.25], "unit": "dimensionless"}

Answer: 1.4

Answer: -2.25

Prompt: A line passes through points (9.5, 11.05) and (23.5, 30.65). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. 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 field worksheet case 171647, 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 weighted_sum_005398(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_005398"}

Answer: python_code

Prompt: Write a Python function weighted_sum_005398(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_005398([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.18 and interior values [-1.1, 1.75, -0.4], 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 = 4.5 kg and a = 5.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 25.425, "unit": "N"}

Answer: 25.425

Prompt: A cart has mass 4.5 kg and measured acceleration 5.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 4.5 kg and a = 5.65 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 43.9^2 and multiply by 0.5 * 27.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 26836.3992, "unit": "J"}

Answer: 26836.3992

Prompt: A body of mass 27.85 kg moves at 43.9 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 43.9^2 and multiply by 0.5 * 27.85.
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=69 degrees through the sine of 2 theta.
3. Substitute v=37.7 m/s and g=9.81 m/s^2.
Final: {"answer": 96.9448, "unit": "m"}

Answer: 96.9448

Prompt: A projectile is launched on level ground with no air resistance at speed 37.7 m/s and angle 69 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=69 degrees through the sine of 2 theta.
Substitute v=37.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.99 * 8.314 * 456 / 108.3.
Final: {"answer": 69.6626, "unit": "kPa"}

Answer: 69.6626

Prompt: An ideal gas sample has n=1.99 mol, T=456 K, and V=108.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.99 * 8.314 * 456 / 108.3.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=218.8 V and R=151.7 ohm.
Final: {"answer": 315.5797, "unit": "W"}

Answer: 315.5797

Prompt: A resistor has resistance 151.7 ohm and voltage 218.8 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=218.8 V and R=151.7 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.56 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 244.6956, "unit": "g"}

Answer: 244.6956

Prompt: A sample contains 5.56 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.56 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 325 mL to 0.325 L.
3. Compute M = 4.81 / 0.325.
Final: {"answer": 14.8, "unit": "mol/L"}

Answer: 14.8

Prompt: A solution contains 4.81 mol of solute in 325 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 325 mL to 0.325 L.
Compute M = 4.81 / 0.325.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.59 y with y(0)=20, step size h=1.15, 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) = -0.59 y, so each step multiplies y by 1 - h*0.59.
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(-7.7)=-4.85 and f(-2.3)=8.65.
3. The interval width is 5.4.
Final: {"answer": 10.26, "unit": "area_units"}

Answer: 10.26

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2.5x+14.4 from x=-7.7 to x=-2.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.7)=-4.85 and f(-2.3)=8.65.
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=0.22 and add it to the current value.
Final: {"answer": [-0.369, -0.369, 0.874], "unit": "temperature_units"}

Answer: -0.369

Answer: -0.369

Answer: 0.874

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.25, right=0.2; current interior values are [0.5, -1.7, 2.15]. 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 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4539.5 / 100.
Final: {"answer": 45.395, "unit": "m"}

Answer: 45.395

Prompt: Convert 4539.5 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 4539.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=282 degrees and keep the unit as newtons.
Final: {"answer": [68.4029, -321.8106], "unit": "N"}

Answer: 68.4029

Answer: -321.8106

Prompt: A vector has magnitude 329 N at 282 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=282 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [4.75, -10.75], "unit": "dimensionless"}

Answer: 4.75

Answer: -10.75

Prompt: A line passes through points (6.25, 18.9375) and (9, 32). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In field worksheet case 333421, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 10.7 kg and a = 7.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 77.575, "unit": "N"}

Answer: 77.575

Prompt: A cart has mass 10.7 kg and measured acceleration 7.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 10.7 kg and a = 7.25 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=33 degrees through the sine of 2 theta.
3. Substitute v=82.2 m/s and g=9.81 m/s^2.
Final: {"answer": 629.2233, "unit": "m"}

Answer: 629.2233

Prompt: A projectile is launched on level ground with no air resistance at speed 82.2 m/s and angle 33 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=33 degrees through the sine of 2 theta.
Substitute v=82.2 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 = 0.55 * 8.314 * 489 / 36.4.
Final: {"answer": 61.43, "unit": "kPa"}

Answer: 61.43

Prompt: An ideal gas sample has n=0.55 mol, T=489 K, and V=36.4 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 = 0.55 * 8.314 * 489 / 36.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 260 * 1.72 * 4.
Final: {"answer": 1788.8, "unit": "J"}

Answer: 1788.8

Prompt: A 260 g sample has specific heat 1.72 J/(g*K). How much heat is needed to raise its temperature by 4 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 260 * 1.72 * 4.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=197.3 V and R=12.9 ohm.
Final: {"answer": 3017.6194, "unit": "W"}

Answer: 3017.6194

Prompt: A resistor has resistance 12.9 ohm and voltage 197.3 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=197.3 V and R=12.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=108 mg, t=230 h, and T_half=65 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 9.2948, "unit": "mg"}

Answer: 9.2948

Prompt: A radioactive sample starts with 108 mg. Its half-life is 65 hours. How many mg remain after 230 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=108 mg, t=230 h, and T_half=65 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 = 1.1 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 198.1716, "unit": "g"}

Answer: 198.1716

Prompt: A sample contains 1.1 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 = 1.1 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 1430 mL to 1.43 L.
3. Compute M = 2.52 / 1.43.
Final: {"answer": 1.7622, "unit": "mol/L"}

Answer: 1.7622

Prompt: A solution contains 2.52 mol of solute in 1430 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1430 mL to 1.43 L.
Compute M = 2.52 / 1.43.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.96 y, so each step multiplies y by 1 - h*0.96.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": -0.2307, "unit": "state_units"}

Answer: -0.2307

Prompt: Use explicit Euler on dy/dt = -0.96 y with y(0)=35, step size h=1.55, 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) = -0.96 y, so each step multiplies y by 1 - h*0.96.
Apply that update for 7 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-8.2)=-10.3 and f(0.5)=-10.3.
3. The interval width is 8.7.
Final: {"answer": -89.61, "unit": "area_units"}

Answer: -89.61

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0x+-10.3 from x=-8.2 to x=0.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-8.2)=-10.3 and f(0.5)=-10.3.
The interval width is 8.7.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.06 and add it to the current value.
Final: {"answer": [-0.383, 1.985, 2.215], "unit": "temperature_units"}

Answer: -0.383

Answer: 1.985

Answer: 2.215

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1, right=2.5; current interior values are [-0.65, 2.15, 2.2]. 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. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=326 degrees and keep the unit as newtons.
Final: {"answer": [118.9669, -80.2442], "unit": "N"}

Answer: 118.9669

Answer: -80.2442

Prompt: A vector has magnitude 143.5 N at 326 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=326 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-5.1, -21.5], "unit": "dimensionless"}

Answer: -5.1

Answer: -21.5

Prompt: A line passes through points (1, -26.6) and (14.25, -94.175). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In simulation spec case 237901, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def safe_mean_005434(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_005434"}

Answer: python_code

Prompt: Write a Python function safe_mean_005434(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_005434([])
    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 warehouse survey records in release 283515, 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. 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=6 m/s and g=9.81 m/s^2.
Final: {"answer": 1.2551, "unit": "m"}

Answer: 1.2551

Prompt: A projectile is launched on level ground with no air resistance at speed 6 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=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 = 4.67 * 8.314 * 365 / 75.2.
Final: {"answer": 188.4525, "unit": "kPa"}

Answer: 188.4525

Prompt: An ideal gas sample has n=4.67 mol, T=365 K, and V=75.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.67 * 8.314 * 365 / 75.2.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=95.4 V and R=17.1 ohm.
Final: {"answer": 532.2316, "unit": "W"}

Answer: 532.2316

Prompt: A resistor has resistance 17.1 ohm and voltage 95.4 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=95.4 V and R=17.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=82.5 mg, t=144 h, and T_half=64.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 17.5544, "unit": "mg"}

Answer: 17.5544

Prompt: A radioactive sample starts with 82.5 mg. Its half-life is 64.5 hours. How many mg remain after 144 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=82.5 mg, t=144 h, and T_half=64.5 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 = 1.48 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 86.4912, "unit": "g"}

Answer: 86.4912

Prompt: A sample contains 1.48 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 = 1.48 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 2690 mL to 2.69 L.
3. Compute M = 1.475 / 2.69.
Final: {"answer": 0.5483, "unit": "mol/L"}

Answer: 0.5483

Prompt: A solution contains 1.475 mol of solute in 2690 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2690 mL to 2.69 L.
Compute M = 1.475 / 2.69.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.45 y, so each step multiplies y by 1 - h*0.45.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.45 y with y(0)=20.5, step size h=1.65, 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) = -0.45 y, so each step multiplies y by 1 - h*0.45.
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(-9.8)=66.32 and f(-0.7)=-1.02.
3. The interval width is 9.1.
Final: {"answer": 297.115, "unit": "area_units"}

Answer: 297.115

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.4x+-6.2 from x=-9.8 to x=-0.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.8)=66.32 and f(-0.7)=-1.02.
The interval width is 9.1.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.08 and add it to the current value.
Final: {"answer": [0.824, 1.54, 2.512], "unit": "temperature_units"}

Answer: 0.824

Answer: 1.54

Answer: 2.512

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.45, right=0.5; current interior values are [0.7, 1.5, 2.8]. Use r=0.08. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.08 and add it to the current value.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=171 degrees and keep the unit as newtons.
Final: {"answer": [-393.1, 62.2609], "unit": "N"}

Answer: -393.1

Answer: 62.2609

Prompt: A vector has magnitude 398 N at 171 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=171 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-5.65, 30.0], "unit": "dimensionless"}

Answer: -5.65

Answer: 30.0

Prompt: A line passes through points (-3, 46.95) and (2.75, 14.4625). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In instrument manual case 93857, 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_005452(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_005452"}

Answer: python_code

Prompt: Write a Python function center_values_005452(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_005452([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.46 and interior values [-1.5, 2.3, 1.25], 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 = 19.95 kg and a = 4.05 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 80.7975, "unit": "N"}

Answer: 80.7975

Prompt: A cart has mass 19.95 kg and measured acceleration 4.05 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 = 19.95 kg and a = 4.05 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 = 34.5^2 and multiply by 0.5 * 20.55.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 12229.8188, "unit": "J"}

Answer: 12229.8188

Prompt: A body of mass 20.55 kg moves at 34.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 34.5^2 and multiply by 0.5 * 20.55.
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=34 degrees through the sine of 2 theta.
3. Substitute v=50.7 m/s and g=9.81 m/s^2.
Final: {"answer": 242.9477, "unit": "m"}

Answer: 242.9477

Prompt: A projectile is launched on level ground with no air resistance at speed 50.7 m/s and angle 34 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=34 degrees through the sine of 2 theta.
Substitute v=50.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.76 * 8.314 * 454 / 114.4.
Final: {"answer": 58.0701, "unit": "kPa"}

Answer: 58.0701

Prompt: An ideal gas sample has n=1.76 mol, T=454 K, and V=114.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.76 * 8.314 * 454 / 114.4.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=166.8 V and R=110.5 ohm.
Final: {"answer": 251.785, "unit": "W"}

Answer: 251.785

Prompt: A resistor has resistance 110.5 ohm and voltage 166.8 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=166.8 V and R=110.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=523.5 mg, t=246 h, and T_half=101.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 97.5723, "unit": "mg"}

Answer: 97.5723

Prompt: A radioactive sample starts with 523.5 mg. Its half-life is 101.5 hours. How many mg remain after 246 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=523.5 mg, t=246 h, and T_half=101.5 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 = 2.98 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 298.2593, "unit": "g"}

Answer: 298.2593

Prompt: A sample contains 2.98 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 = 2.98 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 3265 mL to 3.265 L.
3. Compute M = 3.135 / 3.265.
Final: {"answer": 0.9602, "unit": "mol/L"}

Answer: 0.9602

Prompt: A solution contains 3.135 mol of solute in 3265 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3265 mL to 3.265 L.
Compute M = 3.135 / 3.265.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 0.0545, "unit": "state_units"}

Answer: 0.0545

Prompt: Use explicit Euler on dy/dt = -0.32 y with y(0)=72.5, step size h=1.5, for 11 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.
Apply that update for 11 steps and round the final state.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 22640.0 / 1000.
Final: {"answer": 22.64, "unit": "kg"}

Answer: 22.64

Prompt: Convert 22640 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 22640.0 / 1000.


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 125187, 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 pairwise_ratios_005470(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_005470"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_005470(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_005470([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_005470([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: target_schema, valid_examples.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each mobile survey record from batch 521439 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 7.35 kg and a = 2.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 16.905, "unit": "N"}

Answer: 16.905

Prompt: A cart has mass 7.35 kg and measured acceleration 2.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 7.35 kg and a = 2.3 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=54 degrees through the sine of 2 theta.
3. Substitute v=63 m/s and g=9.81 m/s^2.
Final: {"answer": 384.7853, "unit": "m"}

Answer: 384.7853

Prompt: A projectile is launched on level ground with no air resistance at speed 63 m/s and angle 54 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=54 degrees through the sine of 2 theta.
Substitute v=63 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 = 4.81 * 8.314 * 477 / 111.7.
Final: {"answer": 170.7734, "unit": "kPa"}

Answer: 170.7734

Prompt: An ideal gas sample has n=4.81 mol, T=477 K, and V=111.7 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 = 4.81 * 8.314 * 477 / 111.7.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1010 * 1.745 * 21.
Final: {"answer": 37011.45, "unit": "J"}

Answer: 37011.45

Prompt: A 1010 g sample has specific heat 1.745 J/(g*K). How much heat is needed to raise its temperature by 21 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1010 * 1.745 * 21.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=724 mg, t=347 h, and T_half=120 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 97.5574, "unit": "mg"}

Answer: 97.5574

Prompt: A radioactive sample starts with 724 mg. Its half-life is 120 hours. How many mg remain after 347 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=724 mg, t=347 h, and T_half=120 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.46 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 20.2446, "unit": "g"}

Answer: 20.2446

Prompt: A sample contains 0.46 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.46 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4095 mL to 4.095 L.
3. Compute M = 4.955 / 4.095.
Final: {"answer": 1.21, "unit": "mol/L"}

Answer: 1.21

Prompt: A solution contains 4.955 mol of solute in 4095 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4095 mL to 4.095 L.
Compute M = 4.955 / 4.095.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 20.8372, "unit": "state_units"}

Answer: 20.8372

Prompt: Use explicit Euler on dy/dt = -0.11 y with y(0)=38, step size h=1.65, for 3 steps. What is y after the final step?

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


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(2.4)=15.82 and f(10.9)=82.12.
3. The interval width is 8.5.
Final: {"answer": 416.245, "unit": "area_units"}

Answer: 416.245

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.8x+-2.9 from x=2.4 to x=10.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(2.4)=15.82 and f(10.9)=82.12.
The interval width is 8.5.


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=0.1 and add it to the current value.
Final: {"answer": [0.875, -0.71, 2.205], "unit": "temperature_units"}

Answer: 0.875

Answer: -0.71

Answer: 2.205

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.7, right=2.2; current interior values are [1.05, -1.35, 2.65]. Use r=0.1. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 110.5 / 100.
Final: {"answer": 1.105, "unit": "m"}

Answer: 1.105

Prompt: Convert 110.5 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 110.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=106 degrees and keep the unit as newtons.
Final: {"answer": [-63.5344, 221.5708], "unit": "N"}

Answer: -63.5344

Answer: 221.5708

Prompt: A vector has magnitude 230.5 N at 106 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=106 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": [3.2, 20.75], "unit": "dimensionless"}

Answer: 3.2

Answer: 20.75

Prompt: A line passes through points (-15.75, -29.65) and (-5.75, 2.35). Return [slope, intercept] for y = slope*x + intercept.

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


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

```python
def safe_mean_005488(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_005488"}

Answer: python_code

Prompt: Write a Python function safe_mean_005488(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_005488([])
    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 sensor record from batch 449099 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 = 5.05 kg and a = 11 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 55.55, "unit": "N"}

Answer: 55.55

Prompt: A cart has mass 5.05 kg and measured acceleration 11 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 5.05 kg and a = 11 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 = 37.1^2 and multiply by 0.5 * 13.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 8981.0753, "unit": "J"}

Answer: 8981.0753

Prompt: A body of mass 13.05 kg moves at 37.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 37.1^2 and multiply by 0.5 * 13.05.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=76 degrees through the sine of 2 theta.
3. Substitute v=54.8 m/s and g=9.81 m/s^2.
Final: {"answer": 143.7148, "unit": "m"}

Answer: 143.7148

Prompt: A projectile is launched on level ground with no air resistance at speed 54.8 m/s and angle 76 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=76 degrees through the sine of 2 theta.
Substitute v=54.8 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 = 2.51 * 8.314 * 377 / 39.2.
Final: {"answer": 200.6961, "unit": "kPa"}

Answer: 200.6961

Prompt: An ideal gas sample has n=2.51 mol, T=377 K, and V=39.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.51 * 8.314 * 377 / 39.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1445 * 1.055 * 1.
Final: {"answer": 1524.475, "unit": "J"}

Answer: 1524.475

Prompt: A 1445 g sample has specific heat 1.055 J/(g*K). How much heat is needed to raise its temperature by 1 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1445 * 1.055 * 1.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=148.5 V and R=2.5 ohm.
Final: {"answer": 8820.9, "unit": "W"}

Answer: 8820.9

Prompt: A resistor has resistance 2.5 ohm and voltage 148.5 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=148.5 V and R=2.5 ohm.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4465 mL to 4.465 L.
3. Compute M = 3.28 / 4.465.
Final: {"answer": 0.7346, "unit": "mol/L"}

Answer: 0.7346

Prompt: A solution contains 3.28 mol of solute in 4465 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4465 mL to 4.465 L.
Compute M = 3.28 / 4.465.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-2.8)=1.22 and f(-0.4)=-2.14.
3. The interval width is 2.4.
Final: {"answer": -1.104, "unit": "area_units"}

Answer: -1.104

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.4x+-2.7 from x=-2.8 to x=-0.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-2.8)=1.22 and f(-0.4)=-2.14.
The interval width is 2.4.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 29.5 + 273.15.
Final: {"answer": 302.65, "unit": "K"}

Answer: 302.65

Prompt: Convert 29.5 degC to K. Return the converted value with unit.

Kelvin equals Celsius plus 273.15.
Apply the conversion factor directly to the given value.
Compute 29.5 + 273.15.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [9.4, -13.5], "unit": "dimensionless"}

Answer: 9.4

Answer: -13.5

Prompt: A line passes through points (4, 24.1) and (15.25, 129.85). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In quality-control check case 936103, 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 running_total_005506(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_005506"}

Answer: python_code

Prompt: Write a Python function running_total_005506(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

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


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

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=24.5 and h=0.3, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 20.85 kg and a = 5.4 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 112.59, "unit": "N"}

Answer: 112.59

Prompt: A cart has mass 20.85 kg and measured acceleration 5.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 20.85 kg and a = 5.4 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 17.15^2 and multiply by 0.5 * 17.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2500.0412, "unit": "J"}

Answer: 2500.0412

Prompt: A body of mass 17 kg moves at 17.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 17.15^2 and multiply by 0.5 * 17.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=25 degrees through the sine of 2 theta.
3. Substitute v=6.7 m/s and g=9.81 m/s^2.
Final: {"answer": 3.5054, "unit": "m"}

Answer: 3.5054

Prompt: A projectile is launched on level ground with no air resistance at speed 6.7 m/s and angle 25 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=25 degrees through the sine of 2 theta.
Substitute v=6.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.32 * 8.314 * 581 / 92.3.
Final: {"answer": 121.415, "unit": "kPa"}

Answer: 121.415

Prompt: An ideal gas sample has n=2.32 mol, T=581 K, and V=92.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.32 * 8.314 * 581 / 92.3.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=226.5 V and R=30.3 ohm.
Final: {"answer": 1693.1436, "unit": "W"}

Answer: 1693.1436

Prompt: A resistor has resistance 30.3 ohm and voltage 226.5 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=226.5 V and R=30.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=192 mg, t=192.5 h, and T_half=102 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 51.9016, "unit": "mg"}

Answer: 51.9016

Prompt: A radioactive sample starts with 192 mg. Its half-life is 102 hours. How many mg remain after 192.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=192 mg, t=192.5 h, and T_half=102 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 = 6.98 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 307.1898, "unit": "g"}

Answer: 307.1898

Prompt: A sample contains 6.98 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 = 6.98 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 3930 mL to 3.93 L.
3. Compute M = 0.245 / 3.93.
Final: {"answer": 0.0623, "unit": "mol/L"}

Answer: 0.0623

Prompt: A solution contains 0.245 mol of solute in 3930 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3930 mL to 3.93 L.
Compute M = 0.245 / 3.93.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.48 y, so each step multiplies y by 1 - h*0.48.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.4665, "unit": "state_units"}

Answer: 0.4665

Prompt: Use explicit Euler on dy/dt = -0.48 y with y(0)=18, step size h=0.95, 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) = -0.48 y, so each step multiplies y by 1 - h*0.48.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-9.4)=-5.76 and f(0.1)=2.79.
3. The interval width is 9.5.
Final: {"answer": -14.1075, "unit": "area_units"}

Answer: -14.1075

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.9x+2.7 from x=-9.4 to x=0.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.4)=-5.76 and f(0.1)=2.79.
The interval width is 9.5.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 43201.0 / 1000.
Final: {"answer": 43.201, "unit": "kg"}

Answer: 43.201

Prompt: Convert 43201 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 43201.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=26 degrees and keep the unit as newtons.
Final: {"answer": [3.5952, 1.7535], "unit": "N"}

Answer: 3.5952

Answer: 1.7535

Prompt: A vector has magnitude 4 N at 26 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=26 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": [1.05, -27.75], "unit": "dimensionless"}

Answer: 1.05

Answer: -27.75

Prompt: A line passes through points (-10.25, -38.5125) and (-6.75, -34.8375). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In quality-control check case 24095, 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 normalize_005524(values):
    total = sum(values)
    if total == 0:
        raise ValueError('cannot normalize zero-sum values')
    return [v / total for v in values]
```
Final: {"answer": "python_code", "function": "normalize_005524"}

Answer: python_code

Prompt: Write a Python function normalize_005524(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.

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

out = normalize_005524([2, 3, 5]); assert len(out) == 3

try:
    normalize_005524([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 24.15 kg and a = 9.15 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 220.9725, "unit": "N"}

Answer: 220.9725

Prompt: A cart has mass 24.15 kg and measured acceleration 9.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 24.15 kg and a = 9.15 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 1.35^2 and multiply by 0.5 * 18.5.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 16.8581, "unit": "J"}

Answer: 16.8581

Prompt: A body of mass 18.5 kg moves at 1.35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 1.35^2 and multiply by 0.5 * 18.5.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.4 * 8.314 * 397 / 106.4.
Final: {"answer": 74.4509, "unit": "kPa"}

Answer: 74.4509

Prompt: An ideal gas sample has n=2.4 mol, T=397 K, and V=106.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.4 * 8.314 * 397 / 106.4.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=152.7 V and R=5.3 ohm.
Final: {"answer": 4399.4887, "unit": "W"}

Answer: 4399.4887

Prompt: A resistor has resistance 5.3 ohm and voltage 152.7 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=152.7 V and R=5.3 ohm.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 760 mL to 0.76 L.
3. Compute M = 0.73 / 0.76.
Final: {"answer": 0.9605, "unit": "mol/L"}

Answer: 0.9605

Prompt: A solution contains 0.73 mol of solute in 760 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 760 mL to 0.76 L.
Compute M = 0.73 / 0.76.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.07 y, so each step multiplies y by 1 - h*0.07.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 3.0459, "unit": "state_units"}

Answer: 3.0459

Prompt: Use explicit Euler on dy/dt = -0.07 y with y(0)=7, step size h=1.85, 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) = -0.07 y, so each step multiplies y by 1 - h*0.07.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-3.1)=3.72 and f(-2.6)=6.12.
3. The interval width is 0.5.
Final: {"answer": 2.46, "unit": "area_units"}

Answer: 2.46

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.8x+18.6 from x=-3.1 to x=-2.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-3.1)=3.72 and f(-2.6)=6.12.
The interval width is 0.5.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 2627.0 / 100.
Final: {"answer": 26.27, "unit": "m"}

Answer: 26.27

Prompt: Convert 2627 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 2627.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=330 degrees and keep the unit as newtons.
Final: {"answer": [92.2317, -53.25], "unit": "N"}

Answer: 92.2317

Answer: -53.25

Prompt: A vector has magnitude 106.5 N at 330 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=330 degrees and keep the unit as newtons.


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

Answer: consistent

Prompt: In field worksheet case 197464, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each field invoice record from batch 827211 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 = 2.95 kg and a = 10.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 31.7125, "unit": "N"}

Answer: 31.7125

Prompt: A cart has mass 2.95 kg and measured acceleration 10.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 2.95 kg and a = 10.75 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 35.75^2 and multiply by 0.5 * 4.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2747.8344, "unit": "J"}

Answer: 2747.8344

Prompt: A body of mass 4.3 kg moves at 35.75 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 35.75^2 and multiply by 0.5 * 4.3.
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=31 degrees through the sine of 2 theta.
3. Substitute v=31.1 m/s and g=9.81 m/s^2.
Final: {"answer": 87.0536, "unit": "m"}

Answer: 87.0536

Prompt: A projectile is launched on level ground with no air resistance at speed 31.1 m/s and angle 31 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=31 degrees through the sine of 2 theta.
Substitute v=31.1 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 = 3.12 * 8.314 * 398 / 102.0.
Final: {"answer": 101.2156, "unit": "kPa"}

Answer: 101.2156

Prompt: An ideal gas sample has n=3.12 mol, T=398 K, and V=102.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.12 * 8.314 * 398 / 102.0.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=179.7 V and R=166.9 ohm.
Final: {"answer": 193.4817, "unit": "W"}

Answer: 193.4817

Prompt: A resistor has resistance 166.9 ohm and voltage 179.7 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=179.7 V and R=166.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=636.5 mg, t=153 h, and T_half=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 636.5 mg. Its half-life is 5 hours. How many mg remain after 153 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=636.5 mg, t=153 h, and T_half=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 = 4.33 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 433.3767, "unit": "g"}

Answer: 433.3767

Prompt: A sample contains 4.33 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.33 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(6.4)=-46.86 and f(7)=-50.4.
3. The interval width is 0.6.
Final: {"answer": -29.178, "unit": "area_units"}

Answer: -29.178

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.9x+-9.1 from x=6.4 to x=7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.4)=-46.86 and f(7)=-50.4.
The interval width is 0.6.


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=0.22 and add it to the current value.
Final: {"answer": [0.746, 1.042, -0.15], "unit": "temperature_units"}

Answer: 0.746

Answer: 1.042

Answer: -0.15

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.65, right=-1.65; current interior values are [1.45, 1.35, -0.15]. 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 31844.0 / 1000.
Final: {"answer": 31.844, "unit": "kg"}

Answer: 31.844

Prompt: Convert 31844 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 31844.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=17 degrees and keep the unit as newtons.
Final: {"answer": [144.402, 44.1481], "unit": "N"}

Answer: 144.402

Answer: 44.1481

Prompt: A vector has magnitude 151 N at 17 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=17 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-8.0, -24.0], "unit": "dimensionless"}

Answer: -8.0

Answer: -24.0

Prompt: A line passes through points (14.5, -140) and (16.75, -158). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In lab notebook case 466428, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def center_values_005560(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_005560"}

Answer: python_code

Prompt: Write a Python function center_values_005560(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_005560([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=2.15 mol and T=373 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 = 25.45^2 and multiply by 0.5 * 28.65.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 9278.3383, "unit": "J"}

Answer: 9278.3383

Prompt: A body of mass 28.65 kg moves at 25.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 25.45^2 and multiply by 0.5 * 28.65.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=25 degrees through the sine of 2 theta.
3. Substitute v=12.8 m/s and g=9.81 m/s^2.
Final: {"answer": 12.794, "unit": "m"}

Answer: 12.794

Prompt: A projectile is launched on level ground with no air resistance at speed 12.8 m/s and angle 25 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=25 degrees through the sine of 2 theta.
Substitute v=12.8 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 = 2.59 * 8.314 * 541 / 66.3.
Final: {"answer": 175.7088, "unit": "kPa"}

Answer: 175.7088

Prompt: An ideal gas sample has n=2.59 mol, T=541 K, and V=66.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.59 * 8.314 * 541 / 66.3.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=5.7 V and R=29.3 ohm.
Final: {"answer": 1.1089, "unit": "W"}

Answer: 1.1089

Prompt: A resistor has resistance 29.3 ohm and voltage 5.7 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=5.7 V and R=29.3 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.49 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 449.3906, "unit": "g"}

Answer: 449.3906

Prompt: A sample contains 4.49 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.49 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) = -0.09 y, so each step multiplies y by 1 - h*0.09.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 26.517, "unit": "state_units"}

Answer: 26.517

Prompt: Use explicit Euler on dy/dt = -0.09 y with y(0)=35, step size h=0.6, 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) = -0.09 y, so each step multiplies y by 1 - h*0.09.
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(1.8)=-22.02 and f(8.4)=-31.26.
3. The interval width is 6.6.
Final: {"answer": -175.824, "unit": "area_units"}

Answer: -175.824

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.4x+-19.5 from x=1.8 to x=8.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.8)=-22.02 and f(8.4)=-31.26.
The interval width is 6.6.


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=0.22 and add it to the current value.
Final: {"answer": [-0.177, 0.902, 0.987], "unit": "temperature_units"}

Answer: -0.177

Answer: 0.902

Answer: 0.987

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.45, right=1.65; current interior values are [-1.75, 2.2, 0.25]. 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -67.5 + 273.15.
Final: {"answer": 205.65, "unit": "K"}

Answer: 205.65

Prompt: Convert -67.5 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 -67.5 + 273.15.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [1.0, -30.0], "unit": "dimensionless"}

Answer: 1.0

Answer: -30.0

Prompt: A line passes through points (-7.5, -37.5) and (-4, -34). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In lab notebook case 18968, 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