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 869217, 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 weighted_sum_004228(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_004228"}

Answer: python_code

Prompt: Write a Python function weighted_sum_004228(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_004228([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: recurrence, objective, tie_breaking_rule.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a knapsack scoring problem with 597 items and budget 94505, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 15.7 kg and a = 3.7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 58.09, "unit": "N"}

Answer: 58.09

Prompt: A cart has mass 15.7 kg and measured acceleration 3.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 15.7 kg and a = 3.7 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 29.55^2 and multiply by 0.5 * 12.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5326.5352, "unit": "J"}

Answer: 5326.5352

Prompt: A body of mass 12.2 kg moves at 29.55 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 29.55^2 and multiply by 0.5 * 12.2.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=62 degrees through the sine of 2 theta.
3. Substitute v=43.6 m/s and g=9.81 m/s^2.
Final: {"answer": 160.6491, "unit": "m"}

Answer: 160.6491

Prompt: A projectile is launched on level ground with no air resistance at speed 43.6 m/s and angle 62 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=62 degrees through the sine of 2 theta.
Substitute v=43.6 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 = 3.19 * 8.314 * 571 / 55.6.
Final: {"answer": 272.3717, "unit": "kPa"}

Answer: 272.3717

Prompt: An ideal gas sample has n=3.19 mol, T=571 K, and V=55.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.19 * 8.314 * 571 / 55.6.


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=205.6 V and R=132.5 ohm.
Final: {"answer": 319.0291, "unit": "W"}

Answer: 319.0291

Prompt: A resistor has resistance 132.5 ohm and voltage 205.6 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=205.6 V and R=132.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=782.5 mg, t=166 h, and T_half=39.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 42.5007, "unit": "mg"}

Answer: 42.5007

Prompt: A radioactive sample starts with 782.5 mg. Its half-life is 39.5 hours. How many mg remain after 166 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=782.5 mg, t=166 h, and T_half=39.5 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 = 0.53 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 53.0461, "unit": "g"}

Answer: 53.0461

Prompt: A sample contains 0.53 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.53 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(-6.1)=-14.28 and f(1.1)=-8.52.
3. The interval width is 7.2.
Final: {"answer": -82.08, "unit": "area_units"}

Answer: -82.08

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.8x+-9.4 from x=-6.1 to x=1.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.1)=-14.28 and f(1.1)=-8.52.
The interval width is 7.2.

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


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.1 and add it to the current value.
Final: {"answer": [-1.19, 1.11, 1.765], "unit": "temperature_units"}

Answer: -1.19

Answer: 1.11

Answer: 1.765

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.7, right=1.05; current interior values are [-2.0, 1.4, 1.9]. 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -38.0 + 273.15.
Final: {"answer": 235.15, "unit": "K"}

Answer: 235.15

Prompt: Convert -38 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 -38.0 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=203 degrees and keep the unit as newtons.
Final: {"answer": [-440.0013, -186.7695], "unit": "N"}

Answer: -440.0013

Answer: -186.7695

Prompt: A vector has magnitude 478 N at 203 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=203 degrees and keep the unit as newtons.

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


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-6.85, 13.5], "unit": "dimensionless"}

Answer: -6.85

Answer: 13.5

Prompt: A line passes through points (3.75, -12.1875) and (15.75, -94.3875). 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. volt squared divided by ohm is watt
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In student derivation case 79729, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def pairwise_ratios_004246(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_004246"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_004246(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_004246([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_004246([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 registry clinical record from batch 983533 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 = 7.65 kg and a = 3.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 27.9225, "unit": "N"}

Answer: 27.9225

Prompt: A cart has mass 7.65 kg and measured acceleration 3.65 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 = 7.65 kg and a = 3.65 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=6.6 m/s and g=9.81 m/s^2.
Final: {"answer": 4.0565, "unit": "m"}

Answer: 4.0565

Prompt: A projectile is launched on level ground with no air resistance at speed 6.6 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=6.6 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 = 5.43 * 8.314 * 484 / 34.3.
Final: {"answer": 637.0318, "unit": "kPa"}

Answer: 637.0318

Prompt: An ideal gas sample has n=5.43 mol, T=484 K, and V=34.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.43 * 8.314 * 484 / 34.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1755 * 2.85 * 74.
Final: {"answer": 370129.5, "unit": "J"}

Answer: 370129.5

Prompt: A 1755 g sample has specific heat 2.85 J/(g*K). How much heat is needed to raise its temperature by 74 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1755 * 2.85 * 74.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=809 mg, t=339.5 h, and T_half=30 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.3172, "unit": "mg"}

Answer: 0.3172

Prompt: A radioactive sample starts with 809 mg. Its half-life is 30 hours. How many mg remain after 339.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=809 mg, t=339.5 h, and T_half=30 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 1700 mL to 1.7 L.
3. Compute M = 1.42 / 1.7.
Final: {"answer": 0.8353, "unit": "mol/L"}

Answer: 0.8353

Prompt: A solution contains 1.42 mol of solute in 1700 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1700 mL to 1.7 L.
Compute M = 1.42 / 1.7.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.54 y, so each step multiplies y by 1 - h*0.54.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 47.8939, "unit": "state_units"}

Answer: 47.8939

Prompt: Use explicit Euler on dy/dt = -0.54 y with y(0)=74, step size h=0.25, 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) = -0.54 y, so each step multiplies y by 1 - h*0.54.
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(-8.4)=-30.48 and f(-3.7)=-17.79.
3. The interval width is 4.7.
Final: {"answer": -113.4345, "unit": "area_units"}

Answer: -113.4345

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2.7x+-7.8 from x=-8.4 to x=-3.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-8.4)=-30.48 and f(-3.7)=-17.79.
The interval width is 4.7.


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=0.04 and add it to the current value.
Final: {"answer": [-1.132, -1.634, -0.582], "unit": "temperature_units"}

Answer: -1.132

Answer: -1.634

Answer: -0.582

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=-0.2; current interior values are [-1.2, -1.7, -0.55]. Use r=0.04. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=43 degrees and keep the unit as newtons.
Final: {"answer": [203.682, 189.9365], "unit": "N"}

Answer: 203.682

Answer: 189.9365

Prompt: A vector has magnitude 278.5 N at 43 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=43 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [9.5, -14.25], "unit": "dimensionless"}

Answer: 9.5

Answer: -14.25

Prompt: A line passes through points (-20, -204.25) and (-15.25, -159.125). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In simulation spec case 888342, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def threshold_flags_004264(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_004264"}

Answer: python_code

Prompt: Write a Python function threshold_flags_004264(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.

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

assert threshold_flags_004264([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_004264([], 5) == []

assert threshold_flags_004264([-1, 0], 0) == [False, True]


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

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 16 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 7.3 kg and a = 12.15 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 88.695, "unit": "N"}

Answer: 88.695

Prompt: A cart has mass 7.3 kg and measured acceleration 12.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 7.3 kg and a = 12.15 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=43 degrees through the sine of 2 theta.
3. Substitute v=74.4 m/s and g=9.81 m/s^2.
Final: {"answer": 562.8824, "unit": "m"}

Answer: 562.8824

Prompt: A projectile is launched on level ground with no air resistance at speed 74.4 m/s and angle 43 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=43 degrees through the sine of 2 theta.
Substitute v=74.4 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 = 3.29 * 8.314 * 301 / 7.5.
Final: {"answer": 1097.7695, "unit": "kPa"}

Answer: 1097.7695

Prompt: An ideal gas sample has n=3.29 mol, T=301 K, and V=7.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.29 * 8.314 * 301 / 7.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1520 * 1.775 * 115.
Final: {"answer": 310270.0, "unit": "J"}

Answer: 310270.0

Prompt: A 1520 g sample has specific heat 1.775 J/(g*K). How much heat is needed to raise its temperature by 115 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1520 * 1.775 * 115.


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=223.2 V and R=72.5 ohm.
Final: {"answer": 687.1481, "unit": "W"}

Answer: 687.1481

Prompt: A resistor has resistance 72.5 ohm and voltage 223.2 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=223.2 V and R=72.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=732.5 mg, t=241.5 h, and T_half=84.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 101.034, "unit": "mg"}

Answer: 101.034

Prompt: A radioactive sample starts with 732.5 mg. Its half-life is 84.5 hours. How many mg remain after 241.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=732.5 mg, t=241.5 h, and T_half=84.5 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 = 1.53 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 67.3353, "unit": "g"}

Answer: 67.3353

Prompt: A sample contains 1.53 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.53 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 2610 mL to 2.61 L.
3. Compute M = 1.18 / 2.61.
Final: {"answer": 0.4521, "unit": "mol/L"}

Answer: 0.4521

Prompt: A solution contains 1.18 mol of solute in 2610 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2610 mL to 2.61 L.
Compute M = 1.18 / 2.61.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-5.1)=28.48 and f(-4.9)=27.12.
3. The interval width is 0.2.
Final: {"answer": 5.56, "unit": "area_units"}

Answer: 5.56

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.8x+-6.2 from x=-5.1 to x=-4.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-5.1)=28.48 and f(-4.9)=27.12.
The interval width is 0.2.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.14 and add it to the current value.
Final: {"answer": [-1.434, -0.428, 1.765], "unit": "temperature_units"}

Answer: -1.434

Answer: -0.428

Answer: 1.765

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.75, right=0.5; current interior values are [-1.7, -0.75, 2.5]. Use r=0.14. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 24512.0 / 1000.
Final: {"answer": 24.512, "unit": "kg"}

Answer: 24.512

Prompt: Convert 24512 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 24512.0 / 1000.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-9.55, 1.25], "unit": "dimensionless"}

Answer: -9.55

Answer: 1.25

Prompt: A line passes through points (12.25, -115.738) and (27, -256.6). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. 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_004282(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_004282"}

Answer: python_code

Prompt: Write a Python function running_total_004282(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: recurrence, objective, tie_breaking_rule.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a segmentation scoring problem with 1083 items and budget 27660, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 18.65 kg and a = 6.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 123.09, "unit": "N"}

Answer: 123.09

Prompt: A cart has mass 18.65 kg and measured acceleration 6.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 18.65 kg and a = 6.6 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 0.9^2 and multiply by 0.5 * 26.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 10.5907, "unit": "J"}

Answer: 10.5907

Prompt: A body of mass 26.15 kg moves at 0.9 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 0.9^2 and multiply by 0.5 * 26.15.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=56 degrees through the sine of 2 theta.
3. Substitute v=79.6 m/s and g=9.81 m/s^2.
Final: {"answer": 598.8568, "unit": "m"}

Answer: 598.8568

Prompt: A projectile is launched on level ground with no air resistance at speed 79.6 m/s and angle 56 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=56 degrees through the sine of 2 theta.
Substitute v=79.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.07 * 8.314 * 342 / 85.0.
Final: {"answer": 35.7932, "unit": "kPa"}

Answer: 35.7932

Prompt: An ideal gas sample has n=1.07 mol, T=342 K, and V=85.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.07 * 8.314 * 342 / 85.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 485 * 2 * 62.
Final: {"answer": 60140.0, "unit": "J"}

Answer: 60140.0

Prompt: A 485 g sample has specific heat 2 J/(g*K). How much heat is needed to raise its temperature by 62 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 485 * 2 * 62.


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=53.5 V and R=75.8 ohm.
Final: {"answer": 37.7606, "unit": "W"}

Answer: 37.7606

Prompt: A resistor has resistance 75.8 ohm and voltage 53.5 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=53.5 V and R=75.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=284.5 mg, t=322 h, and T_half=67 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 10.1705, "unit": "mg"}

Answer: 10.1705

Prompt: A radioactive sample starts with 284.5 mg. Its half-life is 67 hours. How many mg remain after 322 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=284.5 mg, t=322 h, and T_half=67 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.35 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 254.214, "unit": "g"}

Answer: 254.214

Prompt: A sample contains 4.35 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.35 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 2915 mL to 2.915 L.
3. Compute M = 1.33 / 2.915.
Final: {"answer": 0.4563, "unit": "mol/L"}

Answer: 0.4563

Prompt: A solution contains 1.33 mol of solute in 2915 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2915 mL to 2.915 L.
Compute M = 1.33 / 2.915.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.6 y, so each step multiplies y by 1 - h*0.6.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 13.7897, "unit": "state_units"}

Answer: 13.7897

Prompt: Use explicit Euler on dy/dt = -0.6 y with y(0)=30.5, step size h=0.3, for 4 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.6 y, so each step multiplies y by 1 - h*0.6.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.3)=9.07 and f(15.6)=14.74.
3. The interval width is 6.3.
Final: {"answer": 75.0015, "unit": "area_units"}

Answer: 75.0015

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.9x+0.7 from x=9.3 to x=15.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.3)=9.07 and f(15.6)=14.74.
The interval width is 6.3.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3978.5 / 100.
Final: {"answer": 39.785, "unit": "m"}

Answer: 39.785

Prompt: Convert 3978.5 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 3978.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=120 degrees and keep the unit as newtons.
Final: {"answer": [-123.25, 213.4753], "unit": "N"}

Answer: -123.25

Answer: 213.4753

Prompt: A vector has magnitude 246.5 N at 120 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=120 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-7.45, 14.5], "unit": "dimensionless"}

Answer: -7.45

Answer: 14.5

Prompt: A line passes through points (5.75, -28.3375) and (15, -97.25). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In lab notebook case 474100, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def pairwise_ratios_004300(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_004300"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_004300(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_004300([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_004300([1, 2], [1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a alignment scoring problem with 981 items and budget 18770, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 21.1 kg and a = 7.4 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 156.14, "unit": "N"}

Answer: 156.14

Prompt: A cart has mass 21.1 kg and measured acceleration 7.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 21.1 kg and a = 7.4 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 = 38.5^2 and multiply by 0.5 * 13.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 9671.6812, "unit": "J"}

Answer: 9671.6812

Prompt: A body of mass 13.05 kg moves at 38.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 38.5^2 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=73 degrees through the sine of 2 theta.
3. Substitute v=83.6 m/s and g=9.81 m/s^2.
Final: {"answer": 398.387, "unit": "m"}

Answer: 398.387

Prompt: A projectile is launched on level ground with no air resistance at speed 83.6 m/s and angle 73 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=73 degrees through the sine of 2 theta.
Substitute v=83.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.71 * 8.314 * 464 / 88.4.
Final: {"answer": 161.901, "unit": "kPa"}

Answer: 161.901

Prompt: An ideal gas sample has n=3.71 mol, T=464 K, and V=88.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.71 * 8.314 * 464 / 88.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 475 * 2.275 * 7.
Final: {"answer": 7564.375, "unit": "J"}

Answer: 7564.375

Prompt: A 475 g sample has specific heat 2.275 J/(g*K). How much heat is needed to raise its temperature by 7 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 475 * 2.275 * 7.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=70.3 V and R=147.2 ohm.
Final: {"answer": 33.574, "unit": "W"}

Answer: 33.574

Prompt: A resistor has resistance 147.2 ohm and voltage 70.3 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=70.3 V and R=147.2 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=253 mg, t=13 h, and T_half=94 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 229.8734, "unit": "mg"}

Answer: 229.8734

Prompt: A radioactive sample starts with 253 mg. Its half-life is 94 hours. How many mg remain after 13 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=253 mg, t=13 h, and T_half=94 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 = 0.92 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 40.4892, "unit": "g"}

Answer: 40.4892

Prompt: A sample contains 0.92 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 = 0.92 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 3000 mL to 3 L.
3. Compute M = 2.73 / 3.
Final: {"answer": 0.91, "unit": "mol/L"}

Answer: 0.91

Prompt: A solution contains 2.73 mol of solute in 3000 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3000 mL to 3 L.
Compute M = 2.73 / 3.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-5.8)=48.38 and f(1.2)=5.68.
3. The interval width is 7.
Final: {"answer": 189.21, "unit": "area_units"}

Answer: 189.21

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.1x+13 from x=-5.8 to x=1.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-5.8)=48.38 and f(1.2)=5.68.
The interval width is 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=0.12 and add it to the current value.
Final: {"answer": [0.112, 0.956, 0.828], "unit": "temperature_units"}

Answer: 0.112

Answer: 0.956

Answer: 0.828

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.8, right=0.1; current interior values are [0.1, 1.1, 0.9]. Use r=0.12. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 395.5 / 100.
Final: {"answer": 3.955, "unit": "m"}

Answer: 3.955

Prompt: Convert 395.5 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 395.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=179 degrees and keep the unit as newtons.
Final: {"answer": [-468.4286, 8.1765], "unit": "N"}

Answer: -468.4286

Answer: 8.1765

Prompt: A vector has magnitude 468.5 N at 179 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=179 degrees and keep the unit as newtons.


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

```python
def finite_differences_004318(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_004318"}

Answer: python_code

Prompt: Write a Python function finite_differences_004318(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.

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

assert finite_differences_004318([5]) == []

assert finite_differences_004318([]) == []


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

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a alignment scoring problem with 4792 items and budget 34085, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 23.55^2 and multiply by 0.5 * 14.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 4104.0585, "unit": "J"}

Answer: 4104.0585

Prompt: A body of mass 14.8 kg moves at 23.55 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 23.55^2 and multiply by 0.5 * 14.8.
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 = 1.89 * 8.314 * 534 / 77.6.
Final: {"answer": 108.1313, "unit": "kPa"}

Answer: 108.1313

Prompt: An ideal gas sample has n=1.89 mol, T=534 K, and V=77.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.89 * 8.314 * 534 / 77.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 830 * 4.495 * 56.
Final: {"answer": 208927.6, "unit": "J"}

Answer: 208927.6

Prompt: A 830 g sample has specific heat 4.495 J/(g*K). How much heat is needed to raise its temperature by 56 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 830 * 4.495 * 56.


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=191.6 V and R=193.4 ohm.
Final: {"answer": 189.8168, "unit": "W"}

Answer: 189.8168

Prompt: A resistor has resistance 193.4 ohm and voltage 191.6 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=191.6 V and R=193.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=149 mg, t=59.5 h, and T_half=53 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 68.4286, "unit": "mg"}

Answer: 68.4286

Prompt: A radioactive sample starts with 149 mg. Its half-life is 53 hours. How many mg remain after 59.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=149 mg, t=59.5 h, and T_half=53 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.7 y, so each step multiplies y by 1 - h*0.7.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.7 y with y(0)=69.5, step size h=1.3, for 9 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.7 y, so each step multiplies y by 1 - h*0.7.
Apply that update for 9 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6.6)=-41.32 and f(0.3)=4.91.
3. The interval width is 6.9.
Final: {"answer": -125.6145, "unit": "area_units"}

Answer: -125.6145

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.7x+2.9 from x=-6.6 to x=0.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.6)=-41.32 and f(0.3)=4.91.
The interval width is 6.9.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.14 and add it to the current value.
Final: {"answer": [0.455, -1.193, -1.026], "unit": "temperature_units"}

Answer: 0.455

Answer: -1.193

Answer: -1.026

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=3, right=-1.15; current interior values are [0.35, -1.55, -0.9]. Use r=0.14. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=52 degrees and keep the unit as newtons.
Final: {"answer": [32.9379, 42.1586], "unit": "N"}

Answer: 32.9379

Answer: 42.1586

Prompt: A vector has magnitude 53.5 N at 52 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=52 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": [8.4, 12.0], "unit": "dimensionless"}

Answer: 8.4

Answer: 12.0

Prompt: A line passes through points (5.5, 58.2) and (17.5, 159). 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 sensor calibration case 344643, 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 finite_differences_004336(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_004336"}

Answer: python_code

Prompt: Write a Python function finite_differences_004336(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.

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

assert finite_differences_004336([5]) == []

assert finite_differences_004336([]) == []


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

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a segmentation scoring problem with 2504 items and budget 54640, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=16 degrees through the sine of 2 theta.
3. Substitute v=69.3 m/s and g=9.81 m/s^2.
Final: {"answer": 259.4222, "unit": "m"}

Answer: 259.4222

Prompt: A projectile is launched on level ground with no air resistance at speed 69.3 m/s and angle 16 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=16 degrees through the sine of 2 theta.
Substitute v=69.3 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.18 * 8.314 * 420 / 92.6.
Final: {"answer": 6.7877, "unit": "kPa"}

Answer: 6.7877

Prompt: An ideal gas sample has n=0.18 mol, T=420 K, and V=92.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.18 * 8.314 * 420 / 92.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1360 * 1.595 * 78.
Final: {"answer": 169197.6, "unit": "J"}

Answer: 169197.6

Prompt: A 1360 g sample has specific heat 1.595 J/(g*K). How much heat is needed to raise its temperature by 78 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1360 * 1.595 * 78.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=585 mg, t=322.5 h, and T_half=19.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0061, "unit": "mg"}

Answer: 0.0061

Prompt: A radioactive sample starts with 585 mg. Its half-life is 19.5 hours. How many mg remain after 322.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=585 mg, t=322.5 h, and T_half=19.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.88 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 346.7988, "unit": "g"}

Answer: 346.7988

Prompt: A sample contains 7.88 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.88 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 4275 mL to 4.275 L.
3. Compute M = 2.425 / 4.275.
Final: {"answer": 0.5673, "unit": "mol/L"}

Answer: 0.5673

Prompt: A solution contains 2.425 mol of solute in 4275 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4275 mL to 4.275 L.
Compute M = 2.425 / 4.275.


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 8 steps and round the final state.
Final: {"answer": 13.3218, "unit": "state_units"}

Answer: 13.3218

Prompt: Use explicit Euler on dy/dt = -0.11 y with y(0)=43.5, step size h=1.25, for 8 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.
Apply that update for 8 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-4.9)=-28.62 and f(4.9)=18.42.
3. The interval width is 9.8.
Final: {"answer": -49.98, "unit": "area_units"}

Answer: -49.98

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.8x+-5.1 from x=-4.9 to x=4.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-4.9)=-28.62 and f(4.9)=18.42.
The interval width is 9.8.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.08 and add it to the current value.
Final: {"answer": [-1.044, -0.878, 0.06], "unit": "temperature_units"}

Answer: -1.044

Answer: -0.878

Answer: 0.06

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.55, right=-1.45; current interior values are [-1.3, -0.95, 0.3]. Use r=0.08. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=116 degrees and keep the unit as newtons.
Final: {"answer": [-146.416, 300.1972], "unit": "N"}

Answer: -146.416

Answer: 300.1972

Prompt: A vector has magnitude 334 N at 116 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=116 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": [4.05, -3.5], "unit": "dimensionless"}

Answer: 4.05

Answer: -3.5

Prompt: A line passes through points (-15.75, -67.2875) and (-10.75, -47.0375). Return [slope, intercept] for y = slope*x + intercept.

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


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

```python
def center_values_004354(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_004354"}

Answer: python_code

Prompt: Write a Python function center_values_004354(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_004354([])
    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=4.21 mol and T=300 K, but does not give volume. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 25 kg and a = 6.15 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 153.75, "unit": "N"}

Answer: 153.75

Prompt: A cart has mass 25 kg and measured acceleration 6.15 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 = 25 kg and a = 6.15 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 16.1^2 and multiply by 0.5 * 21.65.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2805.9483, "unit": "J"}

Answer: 2805.9483

Prompt: A body of mass 21.65 kg moves at 16.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 16.1^2 and multiply by 0.5 * 21.65.
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=9 degrees through the sine of 2 theta.
3. Substitute v=50.7 m/s and g=9.81 m/s^2.
Final: {"answer": 80.971, "unit": "m"}

Answer: 80.971

Prompt: A projectile is launched on level ground with no air resistance at speed 50.7 m/s and angle 9 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=9 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 = 2.85 * 8.314 * 601 / 118.4.
Final: {"answer": 120.2756, "unit": "kPa"}

Answer: 120.2756

Prompt: An ideal gas sample has n=2.85 mol, T=601 K, and V=118.4 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 = 2.85 * 8.314 * 601 / 118.4.


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=201.1 V and R=129.9 ohm.
Final: {"answer": 311.3257, "unit": "W"}

Answer: 311.3257

Prompt: A resistor has resistance 129.9 ohm and voltage 201.1 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=201.1 V and R=129.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=142 mg, t=8.5 h, and T_half=82.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 132.2127, "unit": "mg"}

Answer: 132.2127

Prompt: A radioactive sample starts with 142 mg. Its half-life is 82.5 hours. How many mg remain after 8.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=142 mg, t=8.5 h, and T_half=82.5 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 = 0.14 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 25.2218, "unit": "g"}

Answer: 25.2218

Prompt: A sample contains 0.14 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 = 0.14 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 2060 mL to 2.06 L.
3. Compute M = 1.065 / 2.06.
Final: {"answer": 0.517, "unit": "mol/L"}

Answer: 0.517

Prompt: A solution contains 1.065 mol of solute in 2060 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2060 mL to 2.06 L.
Compute M = 1.065 / 2.06.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.9)=33.94 and f(15.7)=60.62.
3. The interval width is 5.8.
Final: {"answer": 274.224, "unit": "area_units"}

Answer: 274.224

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.6x+-11.6 from x=9.9 to x=15.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.9)=33.94 and f(15.7)=60.62.
The interval width is 5.8.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.18 and add it to the current value.
Final: {"answer": [-0.857, 0.924, 1.224], "unit": "temperature_units"}

Answer: -0.857

Answer: 0.924

Answer: 1.224

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=-1.1; current interior values are [-2.0, 1.5, 1.8]. Use r=0.18. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 64.5 + 273.15.
Final: {"answer": 337.65, "unit": "K"}

Answer: 337.65

Prompt: Convert 64.5 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 64.5 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=29 degrees and keep the unit as newtons.
Final: {"answer": [386.1446, 214.0434], "unit": "N"}

Answer: 386.1446

Answer: 214.0434

Prompt: A vector has magnitude 441.5 N at 29 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=29 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": [-4.6, 25.75], "unit": "dimensionless"}

Answer: -4.6

Answer: 25.75

Prompt: A line passes through points (14.25, -39.8) and (20, -66.25). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In quality-control check case 296400, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def pairwise_ratios_004372(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_004372"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_004372(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_004372([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_004372([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: launch_angle_or_vertical_velocity.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 23 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 18.85^2 and multiply by 0.5 * 6.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1074.8506, "unit": "J"}

Answer: 1074.8506

Prompt: A body of mass 6.05 kg moves at 18.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 18.85^2 and multiply by 0.5 * 6.05.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=17 degrees through the sine of 2 theta.
3. Substitute v=40.5 m/s and g=9.81 m/s^2.
Final: {"answer": 93.4981, "unit": "m"}

Answer: 93.4981

Prompt: A projectile is launched on level ground with no air resistance at speed 40.5 m/s and angle 17 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=17 degrees through the sine of 2 theta.
Substitute v=40.5 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.37 * 8.314 * 249 / 104.1.
Final: {"answer": 86.9041, "unit": "kPa"}

Answer: 86.9041

Prompt: An ideal gas sample has n=4.37 mol, T=249 K, and V=104.1 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 = 4.37 * 8.314 * 249 / 104.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1615 * 3.73 * 21.
Final: {"answer": 126502.95, "unit": "J"}

Answer: 126502.95

Prompt: A 1615 g sample has specific heat 3.73 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 = 1615 * 3.73 * 21.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=27.3 V and R=10.4 ohm.
Final: {"answer": 71.6625, "unit": "W"}

Answer: 71.6625

Prompt: A resistor has resistance 10.4 ohm and voltage 27.3 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=27.3 V and R=10.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=649 mg, t=255 h, and T_half=63 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 39.2455, "unit": "mg"}

Answer: 39.2455

Prompt: A radioactive sample starts with 649 mg. Its half-life is 63 hours. How many mg remain after 255 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=649 mg, t=255 h, and T_half=63 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.33 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 96.02, "unit": "g"}

Answer: 96.02

Prompt: A sample contains 5.33 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.33 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4540 mL to 4.54 L.
3. Compute M = 0.75 / 4.54.
Final: {"answer": 0.1652, "unit": "mol/L"}

Answer: 0.1652

Prompt: A solution contains 0.75 mol of solute in 4540 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4540 mL to 4.54 L.
Compute M = 0.75 / 4.54.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 0.3797, "unit": "state_units"}

Answer: 0.3797

Prompt: Use explicit Euler on dy/dt = -0.51 y with y(0)=1, step size h=0.2, for 9 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.
Apply that update for 9 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-2.3)=32.27 and f(2.3)=-4.07.
3. The interval width is 4.6.
Final: {"answer": 64.86, "unit": "area_units"}

Answer: 64.86

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.9x+14.1 from x=-2.3 to x=2.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-2.3)=32.27 and f(2.3)=-4.07.
The interval width is 4.6.


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=0.02 and add it to the current value.
Final: {"answer": [-1.755, 1.507, -1.878], "unit": "temperature_units"}

Answer: -1.755

Answer: 1.507

Answer: -1.878

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=-0.6, right=0.45; current interior values are [-1.85, 1.65, -2.0]. Use r=0.02. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4891.5 / 100.
Final: {"answer": 48.915, "unit": "m"}

Answer: 48.915

Prompt: Convert 4891.5 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 4891.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=137 degrees and keep the unit as newtons.
Final: {"answer": [-236.9586, 220.9675], "unit": "N"}

Answer: -236.9586

Answer: 220.9675

Prompt: A vector has magnitude 324 N at 137 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=137 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-7.95, 5.75], "unit": "dimensionless"}

Answer: -7.95

Answer: 5.75

Prompt: A line passes through points (4.25, -28.0375) and (8.25, -59.8375). 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. 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 field worksheet case 534558, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def clamp_004390(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_004390"}

Answer: python_code

Prompt: Write a Python function clamp_004390(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.

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

try:
    clamp_004390(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 16.8^2 and multiply by 0.5 * 12.65.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1785.168, "unit": "J"}

Answer: 1785.168

Prompt: A body of mass 12.65 kg moves at 16.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 16.8^2 and multiply by 0.5 * 12.65.
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=77 degrees through the sine of 2 theta.
3. Substitute v=50.5 m/s and g=9.81 m/s^2.
Final: {"answer": 113.9609, "unit": "m"}

Answer: 113.9609

Prompt: A projectile is launched on level ground with no air resistance at speed 50.5 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=50.5 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.56 * 8.314 * 341 / 16.8.
Final: {"answer": 263.2569, "unit": "kPa"}

Answer: 263.2569

Prompt: An ideal gas sample has n=1.56 mol, T=341 K, and V=16.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.56 * 8.314 * 341 / 16.8.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=180.8 V and R=77.1 ohm.
Final: {"answer": 423.9772, "unit": "W"}

Answer: 423.9772

Prompt: A resistor has resistance 77.1 ohm and voltage 180.8 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=180.8 V and R=77.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=678.5 mg, t=182 h, and T_half=91.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 170.9149, "unit": "mg"}

Answer: 170.9149

Prompt: A radioactive sample starts with 678.5 mg. Its half-life is 91.5 hours. How many mg remain after 182 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=678.5 mg, t=182 h, and T_half=91.5 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 = 0.82 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 147.7279, "unit": "g"}

Answer: 147.7279

Prompt: A sample contains 0.82 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 = 0.82 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 1635 mL to 1.635 L.
3. Compute M = 2.47 / 1.635.
Final: {"answer": 1.5107, "unit": "mol/L"}

Answer: 1.5107

Prompt: A solution contains 2.47 mol of solute in 1635 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1635 mL to 1.635 L.
Compute M = 2.47 / 1.635.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-1)=15.3 and f(1.5)=2.3.
3. The interval width is 2.5.
Final: {"answer": 22.0, "unit": "area_units"}

Answer: 22.0

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.2x+10.1 from x=-1 to x=1.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-1)=15.3 and f(1.5)=2.3.
The interval width is 2.5.


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=0.16 and add it to the current value.
Final: {"answer": [1.216, 0.04, -0.79], "unit": "temperature_units"}

Answer: 1.216

Answer: 0.04

Answer: -0.79

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.65, right=-0.05; current interior values are [1.4, 0.0, -1.15]. Use r=0.16. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=224 degrees and keep the unit as newtons.
Final: {"answer": [-352.8362, -340.7299], "unit": "N"}

Answer: -352.8362

Answer: -340.7299

Prompt: A vector has magnitude 490.5 N at 224 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=224 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": [8.9, 27.0], "unit": "dimensionless"}

Answer: 8.9

Answer: 27.0

Prompt: A line passes through points (-14.5, -102.05) and (-1.25, 15.875). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. 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 lab notebook case 532640, 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. 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=0.16 and interior values [0.35, 2.2, -0.45], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 7.75 kg and a = 14.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 111.9875, "unit": "N"}

Answer: 111.9875

Prompt: A cart has mass 7.75 kg and measured acceleration 14.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 7.75 kg and a = 14.45 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 8.6^2 and multiply by 0.5 * 12.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 471.495, "unit": "J"}

Answer: 471.495

Prompt: A body of mass 12.75 kg moves at 8.6 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 8.6^2 and multiply by 0.5 * 12.75.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=82 degrees through the sine of 2 theta.
3. Substitute v=58.7 m/s and g=9.81 m/s^2.
Final: {"answer": 96.8156, "unit": "m"}

Answer: 96.8156

Prompt: A projectile is launched on level ground with no air resistance at speed 58.7 m/s and angle 82 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=82 degrees through the sine of 2 theta.
Substitute v=58.7 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 = 5.46 * 8.314 * 385 / 15.1.
Final: {"answer": 1157.4079, "unit": "kPa"}

Answer: 1157.4079

Prompt: An ideal gas sample has n=5.46 mol, T=385 K, and V=15.1 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 = 5.46 * 8.314 * 385 / 15.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1610 * 0.685 * 45.
Final: {"answer": 49628.25, "unit": "J"}

Answer: 49628.25

Prompt: A 1610 g sample has specific heat 0.685 J/(g*K). How much heat is needed to raise its temperature by 45 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1610 * 0.685 * 45.


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=105.3 V and R=153.8 ohm.
Final: {"answer": 72.0942, "unit": "W"}

Answer: 72.0942

Prompt: A resistor has resistance 153.8 ohm and voltage 105.3 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=105.3 V and R=153.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=39 mg, t=102 h, and T_half=105 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 19.89, "unit": "mg"}

Answer: 19.89

Prompt: A radioactive sample starts with 39 mg. Its half-life is 105 hours. How many mg remain after 102 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=39 mg, t=102 h, and T_half=105 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 = 2.17 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 390.9385, "unit": "g"}

Answer: 390.9385

Prompt: A sample contains 2.17 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 2.17 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 2400 mL to 2.4 L.
3. Compute M = 0.175 / 2.4.
Final: {"answer": 0.0729, "unit": "mol/L"}

Answer: 0.0729

Prompt: A solution contains 0.175 mol of solute in 2400 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2400 mL to 2.4 L.
Compute M = 0.175 / 2.4.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.54 y, so each step multiplies y by 1 - h*0.54.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 19.5505, "unit": "state_units"}

Answer: 19.5505

Prompt: Use explicit Euler on dy/dt = -0.54 y with y(0)=74, step size h=0.9, for 2 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.54 y, so each step multiplies y by 1 - h*0.54.
Apply that update for 2 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(6.7)=25.95 and f(9.1)=39.15.
3. The interval width is 2.4.
Final: {"answer": 78.12, "unit": "area_units"}

Answer: 78.12

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5.5x+-10.9 from x=6.7 to x=9.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.7)=25.95 and f(9.1)=39.15.
The interval width is 2.4.


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": [2.369, 2.483, 1.743], "unit": "temperature_units"}

Answer: 2.369

Answer: 2.483

Answer: 1.743

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=1.15, right=2.25; current interior values are [2.6, 3.0, 1.05]. 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 10148.0 / 1000.
Final: {"answer": 10.148, "unit": "kg"}

Answer: 10.148

Prompt: Convert 10148 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 10148.0 / 1000.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [2.9, -5.5], "unit": "dimensionless"}

Answer: 2.9

Answer: -5.5

Prompt: A line passes through points (-20, -63.5) and (-18.5, -59.15). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. 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 831068, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def running_total_004426(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_004426"}

Answer: python_code

Prompt: Write a Python function running_total_004426(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: 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 invoice records in release 242098, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 0.95 kg and a = 1.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 1.8525, "unit": "N"}

Answer: 1.8525

Prompt: A cart has mass 0.95 kg and measured acceleration 1.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 0.95 kg and a = 1.95 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 = 27.7^2 and multiply by 0.5 * 17.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 6752.152, "unit": "J"}

Answer: 6752.152

Prompt: A body of mass 17.6 kg moves at 27.7 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 27.7^2 and multiply by 0.5 * 17.6.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=49 degrees through the sine of 2 theta.
3. Substitute v=34.7 m/s and g=9.81 m/s^2.
Final: {"answer": 121.5466, "unit": "m"}

Answer: 121.5466

Prompt: A projectile is launched on level ground with no air resistance at speed 34.7 m/s and angle 49 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=49 degrees through the sine of 2 theta.
Substitute v=34.7 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 = 0.58 * 8.314 * 522 / 13.6.
Final: {"answer": 185.0843, "unit": "kPa"}

Answer: 185.0843

Prompt: An ideal gas sample has n=0.58 mol, T=522 K, and V=13.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.58 * 8.314 * 522 / 13.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 595 * 1.89 * 70.
Final: {"answer": 78718.5, "unit": "J"}

Answer: 78718.5

Prompt: A 595 g sample has specific heat 1.89 J/(g*K). How much heat is needed to raise its temperature by 70 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 595 * 1.89 * 70.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=999.5 mg, t=255.5 h, and T_half=99.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 168.5723, "unit": "mg"}

Answer: 168.5723

Prompt: A radioactive sample starts with 999.5 mg. Its half-life is 99.5 hours. How many mg remain after 255.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=999.5 mg, t=255.5 h, and T_half=99.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.11 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 56.0266, "unit": "g"}

Answer: 56.0266

Prompt: A sample contains 3.11 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 3.11 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4050 mL to 4.05 L.
3. Compute M = 4.355 / 4.05.
Final: {"answer": 1.0753, "unit": "mol/L"}

Answer: 1.0753

Prompt: A solution contains 4.355 mol of solute in 4050 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4050 mL to 4.05 L.
Compute M = 4.355 / 4.05.