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

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a allocation scoring problem with 1505 items and budget 89045, 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 = 21.4 kg and a = 5.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 127.33, "unit": "N"}

Answer: 127.33

Prompt: A cart has mass 21.4 kg and measured acceleration 5.95 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 = 21.4 kg and a = 5.95 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.24 * 8.314 * 392 / 33.7.
Final: {"answer": 506.7543, "unit": "kPa"}

Answer: 506.7543

Prompt: An ideal gas sample has n=5.24 mol, T=392 K, and V=33.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.24 * 8.314 * 392 / 33.7.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1825 * 3.455 * 110.
Final: {"answer": 693591.25, "unit": "J"}

Answer: 693591.25

Prompt: A 1825 g sample has specific heat 3.455 J/(g*K). How much heat is needed to raise its temperature by 110 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1825 * 3.455 * 110.


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=190.9 V and R=198.3 ohm.
Final: {"answer": 183.7761, "unit": "W"}

Answer: 183.7761

Prompt: A resistor has resistance 198.3 ohm and voltage 190.9 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=190.9 V and R=198.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=101.5 mg, t=239 h, and T_half=15.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0023, "unit": "mg"}

Answer: 0.0023

Prompt: A radioactive sample starts with 101.5 mg. Its half-life is 15.5 hours. How many mg remain after 239 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=101.5 mg, t=239 h, and T_half=15.5 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 410 mL to 0.41 L.
3. Compute M = 2.785 / 0.41.
Final: {"answer": 6.7927, "unit": "mol/L"}

Answer: 6.7927

Prompt: A solution contains 2.785 mol of solute in 410 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 410 mL to 0.41 L.
Compute M = 2.785 / 0.41.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.46 y, so each step multiplies y by 1 - h*0.46.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.001, "unit": "state_units"}

Answer: 0.001

Prompt: Use explicit Euler on dy/dt = -0.46 y with y(0)=40.5, step size h=1.8, for 6 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.46 y, so each step multiplies y by 1 - h*0.46.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6.3)=-38.47 and f(-2)=-17.4.
3. The interval width is 4.3.
Final: {"answer": -120.1205, "unit": "area_units"}

Answer: -120.1205

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.9x+-7.6 from x=-6.3 to x=-2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.3)=-38.47 and f(-2)=-17.4.
The interval width is 4.3.

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


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": [-0.35, 29.5], "unit": "dimensionless"}

Answer: -0.35

Answer: 29.5

Prompt: A line passes through points (-12.75, 33.9625) and (-8.5, 32.475). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. coulomb per second is ampere
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In model card equation case 284724, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
coulomb per second is ampere
The equation is valid only if both sides have identical dimensions.

Answer: consistent


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

```python
def threshold_flags_003580(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_003580"}

Answer: python_code

Prompt: Write a Python function threshold_flags_003580(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_003580([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_003580([], 5) == []

assert threshold_flags_003580([-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: rate_constant, number_of_steps.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=74.5 and h=1.85, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 23 kg and a = 12.7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 292.1, "unit": "N"}

Answer: 292.1

Prompt: A cart has mass 23 kg and measured acceleration 12.7 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 = 23 kg and a = 12.7 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=24 degrees through the sine of 2 theta.
3. Substitute v=13.5 m/s and g=9.81 m/s^2.
Final: {"answer": 13.8061, "unit": "m"}

Answer: 13.8061

Prompt: A projectile is launched on level ground with no air resistance at speed 13.5 m/s and angle 24 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=24 degrees through the sine of 2 theta.
Substitute v=13.5 m/s and g=9.81 m/s^2.

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


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.85 * 8.314 * 602 / 80.3.
Final: {"answer": 115.3089, "unit": "kPa"}

Answer: 115.3089

Prompt: An ideal gas sample has n=1.85 mol, T=602 K, and V=80.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.85 * 8.314 * 602 / 80.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1500 * 1.9 * 20.
Final: {"answer": 57000.0, "unit": "J"}

Answer: 57000.0

Prompt: A 1500 g sample has specific heat 1.9 J/(g*K). How much heat is needed to raise its temperature by 20 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1500 * 1.9 * 20.


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=122.9 V and R=52.9 ohm.
Final: {"answer": 285.5276, "unit": "W"}

Answer: 285.5276

Prompt: A resistor has resistance 52.9 ohm and voltage 122.9 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=122.9 V and R=52.9 ohm.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2185 mL to 2.185 L.
3. Compute M = 0.465 / 2.185.
Final: {"answer": 0.2128, "unit": "mol/L"}

Answer: 0.2128

Prompt: A solution contains 0.465 mol of solute in 2185 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2185 mL to 2.185 L.
Compute M = 0.465 / 2.185.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.63 y with y(0)=2, step size h=1.85, 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) = -0.63 y, so each step multiplies y by 1 - h*0.63.
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(-9.3)=30.47 and f(0)=-15.1.
3. The interval width is 9.3.
Final: {"answer": 71.4705, "unit": "area_units"}

Answer: 71.4705

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.9x+-15.1 from x=-9.3 to x=0. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.3)=30.47 and f(0)=-15.1.
The interval width is 9.3.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.24 and add it to the current value.
Final: {"answer": [2.47, 1.75, 1.044], "unit": "temperature_units"}

Answer: 2.47

Answer: 1.75

Answer: 1.044

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.45, right=0.3; current interior values are [2.95, 1.45, 1.2]. Use r=0.24. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3361.0 / 100.
Final: {"answer": 33.61, "unit": "m"}

Answer: 33.61

Prompt: Convert 3361 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 3361.0 / 100.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-2.15, -22.75], "unit": "dimensionless"}

Answer: -2.15

Answer: -22.75

Prompt: A line passes through points (-2.5, -17.375) and (1.25, -25.4375). 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 pairwise_ratios_003598(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_003598"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_003598(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_003598([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_003598([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: 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=0.3 and interior values [2.6, 0.35, 0.95], 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 = 5.45 kg and a = 7.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 41.1475, "unit": "N"}

Answer: 41.1475

Prompt: A cart has mass 5.45 kg and measured acceleration 7.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 5.45 kg and a = 7.55 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 = 16.9^2 and multiply by 0.5 * 0.5.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 71.4025, "unit": "J"}

Answer: 71.4025

Prompt: A body of mass 0.5 kg moves at 16.9 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 16.9^2 and multiply by 0.5 * 0.5.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.62 * 8.314 * 399 / 90.4.
Final: {"answer": 22.7513, "unit": "kPa"}

Answer: 22.7513

Prompt: An ideal gas sample has n=0.62 mol, T=399 K, and V=90.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.62 * 8.314 * 399 / 90.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 365 * 3.565 * 36.
Final: {"answer": 46844.1, "unit": "J"}

Answer: 46844.1

Prompt: A 365 g sample has specific heat 3.565 J/(g*K). How much heat is needed to raise its temperature by 36 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 365 * 3.565 * 36.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=134 mg, t=292 h, and T_half=92 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 14.8478, "unit": "mg"}

Answer: 14.8478

Prompt: A radioactive sample starts with 134 mg. Its half-life is 92 hours. How many mg remain after 292 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=134 mg, t=292 h, and T_half=92 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(7.3)=-48 and f(10.9)=-66.
3. The interval width is 3.6.
Final: {"answer": -205.2, "unit": "area_units"}

Answer: -205.2

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5x+-11.5 from x=7.3 to x=10.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7.3)=-48 and f(10.9)=-66.
The interval width is 3.6.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1440.0 / 100.
Final: {"answer": 14.4, "unit": "m"}

Answer: 14.4

Prompt: Convert 1440 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 1440.0 / 100.


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

Answer: inconsistent

Prompt: In instrument manual case 990126, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def safe_mean_003616(values):
    if not values:
        raise ValueError('safe_mean requires at least one value')
    return sum(values) / len(values)
```
Final: {"answer": "python_code", "function": "safe_mean_003616"}

Answer: python_code

Prompt: Write a Python function safe_mean_003616(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.

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

try:
    safe_mean_003616([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=32.5 and h=1.7, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 18.7 kg and a = 14.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 266.475, "unit": "N"}

Answer: 266.475

Prompt: A cart has mass 18.7 kg and measured acceleration 14.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 18.7 kg and a = 14.25 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 = 18.7^2 and multiply by 0.5 * 21.5.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3759.1675, "unit": "J"}

Answer: 3759.1675

Prompt: A body of mass 21.5 kg moves at 18.7 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 18.7^2 and multiply by 0.5 * 21.5.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=72 degrees through the sine of 2 theta.
3. Substitute v=11.2 m/s and g=9.81 m/s^2.
Final: {"answer": 7.516, "unit": "m"}

Answer: 7.516

Prompt: A projectile is launched on level ground with no air resistance at speed 11.2 m/s and angle 72 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=72 degrees through the sine of 2 theta.
Substitute v=11.2 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.92 * 8.314 * 517 / 25.4.
Final: {"answer": 494.1396, "unit": "kPa"}

Answer: 494.1396

Prompt: An ideal gas sample has n=2.92 mol, T=517 K, and V=25.4 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 = 2.92 * 8.314 * 517 / 25.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1705 * 2.905 * 40.
Final: {"answer": 198121.0, "unit": "J"}

Answer: 198121.0

Prompt: A 1705 g sample has specific heat 2.905 J/(g*K). How much heat is needed to raise its temperature by 40 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1705 * 2.905 * 40.


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=200.2 V and R=187.9 ohm.
Final: {"answer": 213.3052, "unit": "W"}

Answer: 213.3052

Prompt: A resistor has resistance 187.9 ohm and voltage 200.2 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=200.2 V and R=187.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=281 mg, t=141.5 h, and T_half=80 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 82.4631, "unit": "mg"}

Answer: 82.4631

Prompt: A radioactive sample starts with 281 mg. Its half-life is 80 hours. How many mg remain after 141.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=281 mg, t=141.5 h, and T_half=80 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 2665 mL to 2.665 L.
3. Compute M = 4.855 / 2.665.
Final: {"answer": 1.8218, "unit": "mol/L"}

Answer: 1.8218

Prompt: A solution contains 4.855 mol of solute in 2665 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2665 mL to 2.665 L.
Compute M = 4.855 / 2.665.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.18 y, so each step multiplies y by 1 - h*0.18.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 13.6875, "unit": "state_units"}

Answer: 13.6875

Prompt: Use explicit Euler on dy/dt = -0.18 y with y(0)=27, step size h=1.6, 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) = -0.18 y, so each step multiplies y by 1 - h*0.18.
Apply that update for 2 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.48 and add it to the current value.
Final: {"answer": [1.03, 0.756, 0.93], "unit": "temperature_units"}

Answer: 1.03

Answer: 0.756

Answer: 0.93

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.2, right=2.35; current interior values are [2.95, -0.3, -1.35]. Use r=0.48. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 21359.0 / 1000.
Final: {"answer": 21.359, "unit": "kg"}

Answer: 21.359

Prompt: Convert 21359 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 21359.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=136 degrees and keep the unit as newtons.
Final: {"answer": [-241.6982, 233.4052], "unit": "N"}

Answer: -241.6982

Answer: 233.4052

Prompt: A vector has magnitude 336 N at 136 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=136 degrees and keep the unit as newtons.

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


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

Answer: inconsistent

Prompt: In field worksheet case 511262, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=70 and h=1.8, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 21.15^2 and multiply by 0.5 * 28.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 6329.6134, "unit": "J"}

Answer: 6329.6134

Prompt: A body of mass 28.3 kg moves at 21.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 21.15^2 and multiply by 0.5 * 28.3.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=29 degrees through the sine of 2 theta.
3. Substitute v=18.4 m/s and g=9.81 m/s^2.
Final: {"answer": 29.2676, "unit": "m"}

Answer: 29.2676

Prompt: A projectile is launched on level ground with no air resistance at speed 18.4 m/s and angle 29 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=29 degrees through the sine of 2 theta.
Substitute v=18.4 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 = 0.72 * 8.314 * 432 / 99.6.
Final: {"answer": 25.9637, "unit": "kPa"}

Answer: 25.9637

Prompt: An ideal gas sample has n=0.72 mol, T=432 K, and V=99.6 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 = 0.72 * 8.314 * 432 / 99.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1415 * 2.64 * 55.
Final: {"answer": 205458.0, "unit": "J"}

Answer: 205458.0

Prompt: A 1415 g sample has specific heat 2.64 J/(g*K). How much heat is needed to raise its temperature by 55 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1415 * 2.64 * 55.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=145.6 V and R=91.7 ohm.
Final: {"answer": 231.1817, "unit": "W"}

Answer: 231.1817

Prompt: A resistor has resistance 91.7 ohm and voltage 145.6 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=145.6 V and R=91.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=394.5 mg, t=294 h, and T_half=8 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0, "unit": "mg"}

Answer: 0.0

Prompt: A radioactive sample starts with 394.5 mg. Its half-life is 8 hours. How many mg remain after 294 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=394.5 mg, t=294 h, and T_half=8 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 4535 mL to 4.535 L.
3. Compute M = 4.36 / 4.535.
Final: {"answer": 0.9614, "unit": "mol/L"}

Answer: 0.9614

Prompt: A solution contains 4.36 mol of solute in 4535 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4535 mL to 4.535 L.
Compute M = 4.36 / 4.535.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.3969, "unit": "state_units"}

Answer: 0.3969

Prompt: Use explicit Euler on dy/dt = -0.63 y with y(0)=77, step size h=0.65, for 10 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(2.5)=0.45 and f(11.9)=-36.21.
3. The interval width is 9.4.
Final: {"answer": -168.072, "unit": "area_units"}

Answer: -168.072

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.9x+10.2 from x=2.5 to x=11.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(2.5)=0.45 and f(11.9)=-36.21.
The interval width is 9.4.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 415.0 / 100.
Final: {"answer": 4.15, "unit": "m"}

Answer: 4.15

Prompt: Convert 415 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 415.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=152 degrees and keep the unit as newtons.
Final: {"answer": [-221.6198, 117.8374], "unit": "N"}

Answer: -221.6198

Answer: 117.8374

Prompt: A vector has magnitude 251 N at 152 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=152 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [1.6, -27.25], "unit": "dimensionless"}

Answer: 1.6

Answer: -27.25

Prompt: A line passes through points (5.75, -18.05) and (9.25, -12.45). 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 quality-control check case 127393, 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_003652(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_003652"}

Answer: python_code

Prompt: Write a Python function running_total_003652(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: 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 58.3 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 24.05 kg and a = 14.35 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 345.1175, "unit": "N"}

Answer: 345.1175

Prompt: A cart has mass 24.05 kg and measured acceleration 14.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 24.05 kg and a = 14.35 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=55 degrees through the sine of 2 theta.
3. Substitute v=22.6 m/s and g=9.81 m/s^2.
Final: {"answer": 48.9253, "unit": "m"}

Answer: 48.9253

Prompt: A projectile is launched on level ground with no air resistance at speed 22.6 m/s and angle 55 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=55 degrees through the sine of 2 theta.
Substitute v=22.6 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 = 5.58 * 8.314 * 614 / 4.4.
Final: {"answer": 6473.8095, "unit": "kPa"}

Answer: 6473.8095

Prompt: An ideal gas sample has n=5.58 mol, T=614 K, and V=4.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.58 * 8.314 * 614 / 4.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1610 * 2.555 * 69.
Final: {"answer": 283834.95, "unit": "J"}

Answer: 283834.95

Prompt: A 1610 g sample has specific heat 2.555 J/(g*K). How much heat is needed to raise its temperature by 69 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1610 * 2.555 * 69.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=170.2 V and R=36 ohm.
Final: {"answer": 804.6678, "unit": "W"}

Answer: 804.6678

Prompt: A resistor has resistance 36 ohm and voltage 170.2 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=170.2 V and R=36 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=449.5 mg, t=12.5 h, and T_half=8 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 152.1845, "unit": "mg"}

Answer: 152.1845

Prompt: A radioactive sample starts with 449.5 mg. Its half-life is 8 hours. How many mg remain after 12.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=449.5 mg, t=12.5 h, and T_half=8 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) = -0.42 y, so each step multiplies y by 1 - h*0.42.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 0.0564, "unit": "state_units"}

Answer: 0.0564

Prompt: Use explicit Euler on dy/dt = -0.42 y with y(0)=3, step size h=0.85, 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) = -0.42 y, so each step multiplies y by 1 - h*0.42.
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(0.2)=-16.24 and f(1)=-18.4.
3. The interval width is 0.8.
Final: {"answer": -13.856, "unit": "area_units"}

Answer: -13.856

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.7x+-15.7 from x=0.2 to x=1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(0.2)=-16.24 and f(1)=-18.4.
The interval width is 0.8.


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=0.02 and add it to the current value.
Final: {"answer": [2.525, 0.752, -0.897], "unit": "temperature_units"}

Answer: 2.525

Answer: 0.752

Answer: -0.897

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.7, right=2.4; current interior values are [2.6, 0.75, -1.0]. 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 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 36735.0 / 1000.
Final: {"answer": 36.735, "unit": "kg"}

Answer: 36.735

Prompt: Convert 36735 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 36735.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=9 degrees and keep the unit as newtons.
Final: {"answer": [484.4611, 76.7311], "unit": "N"}

Answer: 484.4611

Answer: 76.7311

Prompt: A vector has magnitude 490.5 N at 9 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=9 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": [0.2, 9.75], "unit": "dimensionless"}

Answer: 0.2

Answer: 9.75

Prompt: A line passes through points (-4.5, 8.85) and (8, 11.35). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. 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 sensor calibration case 614084, 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. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: rate_constant, number_of_steps.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=77 and h=1.05, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 8.1^2 and multiply by 0.5 * 29.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 962.8268, "unit": "J"}

Answer: 962.8268

Prompt: A body of mass 29.35 kg moves at 8.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 8.1^2 and multiply by 0.5 * 29.35.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=82 degrees through the sine of 2 theta.
3. Substitute v=19.6 m/s and g=9.81 m/s^2.
Final: {"answer": 10.794, "unit": "m"}

Answer: 10.794

Prompt: A projectile is launched on level ground with no air resistance at speed 19.6 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=19.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.51 * 8.314 * 414 / 4.8.
Final: {"answer": 3234.0421, "unit": "kPa"}

Answer: 3234.0421

Prompt: An ideal gas sample has n=4.51 mol, T=414 K, and V=4.8 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 = 4.51 * 8.314 * 414 / 4.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1250 * 4.635 * 31.
Final: {"answer": 179606.25, "unit": "J"}

Answer: 179606.25

Prompt: A 1250 g sample has specific heat 4.635 J/(g*K). How much heat is needed to raise its temperature by 31 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1250 * 4.635 * 31.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=162.1 V and R=55 ohm.
Final: {"answer": 477.7529, "unit": "W"}

Answer: 477.7529

Prompt: A resistor has resistance 55 ohm and voltage 162.1 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=162.1 V and R=55 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=417.5 mg, t=227 h, and T_half=112.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 103.0967, "unit": "mg"}

Answer: 103.0967

Prompt: A radioactive sample starts with 417.5 mg. Its half-life is 112.5 hours. How many mg remain after 227 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=417.5 mg, t=227 h, and T_half=112.5 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) = -0.34 y, so each step multiplies y by 1 - h*0.34.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.8641, "unit": "state_units"}

Answer: 0.8641

Prompt: Use explicit Euler on dy/dt = -0.34 y with y(0)=10.5, step size h=0.65, for 10 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.34 y, so each step multiplies y by 1 - h*0.34.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(1.1)=8.46 and f(10.8)=-34.22.
3. The interval width is 9.7.
Final: {"answer": -124.936, "unit": "area_units"}

Answer: -124.936

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.4x+13.3 from x=1.1 to x=10.8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.1)=8.46 and f(10.8)=-34.22.
The interval width is 9.7.


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=0.4 and add it to the current value.
Final: {"answer": [1.04, 1.05, 0.11], "unit": "temperature_units"}

Answer: 1.04

Answer: 1.05

Answer: 0.11

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=2.8, right=1.65; current interior values are [2.9, -1.65, 0.55]. Use r=0.4. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 2176.5 / 100.
Final: {"answer": 21.765, "unit": "m"}

Answer: 21.765

Prompt: Convert 2176.5 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 2176.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=277 degrees and keep the unit as newtons.
Final: {"answer": [5.2404, -42.6795], "unit": "N"}

Answer: 5.2404

Answer: -42.6795

Prompt: A vector has magnitude 43 N at 277 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=277 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": [-0.4, -24.5], "unit": "dimensionless"}

Answer: -0.4

Answer: -24.5

Prompt: A line passes through points (13, -29.7) and (13.75, -30). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In field worksheet case 45238, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def clamp_003688(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_003688"}

Answer: python_code

Prompt: Write a Python function clamp_003688(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_003688(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 14.8 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 = 1.9 kg and a = 8.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 16.34, "unit": "N"}

Answer: 16.34

Prompt: A cart has mass 1.9 kg and measured acceleration 8.6 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 = 1.9 kg and a = 8.6 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 = 24.75^2 and multiply by 0.5 * 9.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2940.3, "unit": "J"}

Answer: 2940.3

Prompt: A body of mass 9.6 kg moves at 24.75 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 24.75^2 and multiply by 0.5 * 9.6.
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=33 degrees through the sine of 2 theta.
3. Substitute v=83.8 m/s and g=9.81 m/s^2.
Final: {"answer": 653.957, "unit": "m"}

Answer: 653.957

Prompt: A projectile is launched on level ground with no air resistance at speed 83.8 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=83.8 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1350 * 2.16 * 97.
Final: {"answer": 282852.0, "unit": "J"}

Answer: 282852.0

Prompt: A 1350 g sample has specific heat 2.16 J/(g*K). How much heat is needed to raise its temperature by 97 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1350 * 2.16 * 97.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=10.1 V and R=144.7 ohm.
Final: {"answer": 0.705, "unit": "W"}

Answer: 0.705

Prompt: A resistor has resistance 144.7 ohm and voltage 10.1 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=10.1 V and R=144.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=313 mg, t=215 h, and T_half=3.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0, "unit": "mg"}

Answer: 0.0

Prompt: A radioactive sample starts with 313 mg. Its half-life is 3.5 hours. How many mg remain after 215 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=313 mg, t=215 h, and T_half=3.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.27 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 130.9691, "unit": "g"}

Answer: 130.9691

Prompt: A sample contains 7.27 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 = 7.27 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 4285 mL to 4.285 L.
3. Compute M = 2.155 / 4.285.
Final: {"answer": 0.5029, "unit": "mol/L"}

Answer: 0.5029

Prompt: A solution contains 2.155 mol of solute in 4285 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4285 mL to 4.285 L.
Compute M = 2.155 / 4.285.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 2.2644, "unit": "state_units"}

Answer: 2.2644

Prompt: Use explicit Euler on dy/dt = -0.63 y with y(0)=45.5, step size h=0.45, 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) = -0.63 y, so each step multiplies y by 1 - h*0.63.
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(7.7)=45.71 and f(12.6)=66.78.
3. The interval width is 4.9.
Final: {"answer": 275.6005, "unit": "area_units"}

Answer: 275.6005

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.3x+12.6 from x=7.7 to x=12.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7.7)=45.71 and f(12.6)=66.78.
The interval width is 4.9.


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=0.42 and add it to the current value.
Final: {"answer": [1.872, -1.148, 1.426], "unit": "temperature_units"}

Answer: 1.872

Answer: -1.148

Answer: 1.426

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=2.4, right=1.3; current interior values are [-1.95, 2.8, -1.85]. Use r=0.42. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.42 and add it to the current value.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=298 degrees and keep the unit as newtons.
Final: {"answer": [73.9418, -139.0642], "unit": "N"}

Answer: 73.9418

Answer: -139.0642

Prompt: A vector has magnitude 157.5 N at 298 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=298 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-5.55, 16.5], "unit": "dimensionless"}

Answer: -5.55

Answer: 16.5

Prompt: A line passes through points (6.5, -19.575) and (17.5, -80.625). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. 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 instrument manual case 362388, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def weighted_sum_003706(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_003706"}

Answer: python_code

Prompt: Write a Python function weighted_sum_003706(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_003706([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 2.8 kg and a = 8.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 22.68, "unit": "N"}

Answer: 22.68

Prompt: A cart has mass 2.8 kg and measured acceleration 8.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 2.8 kg and a = 8.1 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 37.1^2 and multiply by 0.5 * 27.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 19166.5093, "unit": "J"}

Answer: 19166.5093

Prompt: A body of mass 27.85 kg moves at 37.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 37.1^2 and multiply by 0.5 * 27.85.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 580 * 0.745 * 77.
Final: {"answer": 33271.7, "unit": "J"}

Answer: 33271.7

Prompt: A 580 g sample has specific heat 0.745 J/(g*K). How much heat is needed to raise its temperature by 77 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 580 * 0.745 * 77.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=180.8 V and R=186.8 ohm.
Final: {"answer": 174.9927, "unit": "W"}

Answer: 174.9927

Prompt: A resistor has resistance 186.8 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=186.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=845.5 mg, t=199.5 h, and T_half=33 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 12.8012, "unit": "mg"}

Answer: 12.8012

Prompt: A radioactive sample starts with 845.5 mg. Its half-life is 33 hours. How many mg remain after 199.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=845.5 mg, t=199.5 h, and T_half=33 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 1000 mL to 1 L.
3. Compute M = 3.06 / 1.
Final: {"answer": 3.06, "unit": "mol/L"}

Answer: 3.06

Prompt: A solution contains 3.06 mol of solute in 1000 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1000 mL to 1 L.
Compute M = 3.06 / 1.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.53 y, so each step multiplies y by 1 - h*0.53.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 21.9619, "unit": "state_units"}

Answer: 21.9619

Prompt: Use explicit Euler on dy/dt = -0.53 y with y(0)=60.5, step size h=0.75, 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) = -0.53 y, so each step multiplies y by 1 - h*0.53.
Apply that update for 2 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.18 and add it to the current value.
Final: {"answer": [-0.649, 1.428, 1.91], "unit": "temperature_units"}

Answer: -0.649

Answer: 1.428

Answer: 1.91

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.2, right=-1.65; current interior values are [-1.9, 1.95, 2.9]. 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. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=136 degrees and keep the unit as newtons.
Final: {"answer": [-205.0118, 197.9776], "unit": "N"}

Answer: -205.0118

Answer: 197.9776

Prompt: A vector has magnitude 285 N at 136 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=136 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": [9.15, 12.5], "unit": "dimensionless"}

Answer: 9.15

Answer: 12.5

Prompt: A line passes through points (4, 49.1) and (4.75, 55.9625). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In sensor calibration case 71420, 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 finite_differences_003724(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_003724"}

Answer: python_code

Prompt: Write a Python function finite_differences_003724(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_003724([5]) == []

assert finite_differences_003724([]) == []


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 4806 items and budget 8920, 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 = 12.95 kg and a = 4.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 55.685, "unit": "N"}

Answer: 55.685

Prompt: A cart has mass 12.95 kg and measured acceleration 4.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 12.95 kg and a = 4.3 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 2.45^2 and multiply by 0.5 * 26.25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 78.7828, "unit": "J"}

Answer: 78.7828

Prompt: A body of mass 26.25 kg moves at 2.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 2.45^2 and multiply by 0.5 * 26.25.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=71 degrees through the sine of 2 theta.
3. Substitute v=35.5 m/s and g=9.81 m/s^2.
Final: {"answer": 79.0915, "unit": "m"}

Answer: 79.0915

Prompt: A projectile is launched on level ground with no air resistance at speed 35.5 m/s and angle 71 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=71 degrees through the sine of 2 theta.
Substitute v=35.5 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.67 * 8.314 * 612 / 79.2.
Final: {"answer": 235.7775, "unit": "kPa"}

Answer: 235.7775

Prompt: An ideal gas sample has n=3.67 mol, T=612 K, and V=79.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.67 * 8.314 * 612 / 79.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1550 * 4.2 * 52.
Final: {"answer": 338520.0, "unit": "J"}

Answer: 338520.0

Prompt: A 1550 g sample has specific heat 4.2 J/(g*K). How much heat is needed to raise its temperature by 52 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1550 * 4.2 * 52.


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=134.3 V and R=22.6 ohm.
Final: {"answer": 798.0748, "unit": "W"}

Answer: 798.0748

Prompt: A resistor has resistance 22.6 ohm and voltage 134.3 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=134.3 V and R=22.6 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=214 mg, t=234 h, and T_half=117.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 53.8165, "unit": "mg"}

Answer: 53.8165

Prompt: A radioactive sample starts with 214 mg. Its half-life is 117.5 hours. How many mg remain after 234 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=214 mg, t=234 h, and T_half=117.5 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 = 7.52 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 330.9552, "unit": "g"}

Answer: 330.9552

Prompt: A sample contains 7.52 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 = 7.52 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 3345 mL to 3.345 L.
3. Compute M = 3.165 / 3.345.
Final: {"answer": 0.9462, "unit": "mol/L"}

Answer: 0.9462

Prompt: A solution contains 3.165 mol of solute in 3345 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3345 mL to 3.345 L.
Compute M = 3.165 / 3.345.


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 8 steps and round the final state.
Final: {"answer": 0.1072, "unit": "state_units"}

Answer: 0.1072

Prompt: Use explicit Euler on dy/dt = -0.51 y with y(0)=21.5, step size h=0.95, 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) = -0.51 y, so each step multiplies y by 1 - h*0.51.
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(3.1)=2.36 and f(4)=-2.5.
3. The interval width is 0.9.
Final: {"answer": -0.063, "unit": "area_units"}

Answer: -0.063

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.4x+19.1 from x=3.1 to x=4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3.1)=2.36 and f(4)=-2.5.
The interval width is 0.9.


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": [-1.689, -0.521, 1.415], "unit": "temperature_units"}

Answer: -1.689

Answer: -0.521

Answer: 1.415

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.7, right=-1.9; current interior values are [-1.85, -0.85, 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. 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": [297.2953, 277.2323], "unit": "N"}

Answer: 297.2953

Answer: 277.2323

Prompt: A vector has magnitude 406.5 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. Compare the dimensions on both sides of the equation.
2. velocity divided by time is acceleration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In simulation spec case 338794, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def weighted_sum_003742(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_003742"}

Answer: python_code

Prompt: Write a Python function weighted_sum_003742(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_003742([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: 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 59.5 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 22.25 kg and a = 6.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 152.4125, "unit": "N"}

Answer: 152.4125

Prompt: A cart has mass 22.25 kg and measured acceleration 6.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 22.25 kg and a = 6.85 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 29.2^2 and multiply by 0.5 * 8.25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3517.14, "unit": "J"}

Answer: 3517.14

Prompt: A body of mass 8.25 kg moves at 29.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 29.2^2 and multiply by 0.5 * 8.25.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=19 degrees through the sine of 2 theta.
3. Substitute v=82.3 m/s and g=9.81 m/s^2.
Final: {"answer": 425.0819, "unit": "m"}

Answer: 425.0819

Prompt: A projectile is launched on level ground with no air resistance at speed 82.3 m/s and angle 19 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=19 degrees through the sine of 2 theta.
Substitute v=82.3 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 = 6 * 8.314 * 296 / 37.0.
Final: {"answer": 399.072, "unit": "kPa"}

Answer: 399.072

Prompt: An ideal gas sample has n=6 mol, T=296 K, and V=37.0 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 = 6 * 8.314 * 296 / 37.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1720 * 0.555 * 53.
Final: {"answer": 50593.8, "unit": "J"}

Answer: 50593.8

Prompt: A 1720 g sample has specific heat 0.555 J/(g*K). How much heat is needed to raise its temperature by 53 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1720 * 0.555 * 53.


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=187.6 V and R=92.7 ohm.
Final: {"answer": 379.6522, "unit": "W"}

Answer: 379.6522

Prompt: A resistor has resistance 92.7 ohm and voltage 187.6 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=187.6 V and R=92.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=168.5 mg, t=289 h, and T_half=77 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 12.4957, "unit": "mg"}

Answer: 12.4957

Prompt: A radioactive sample starts with 168.5 mg. Its half-life is 77 hours. How many mg remain after 289 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=168.5 mg, t=289 h, and T_half=77 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 = 7.77 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1399.8121, "unit": "g"}

Answer: 1399.8121

Prompt: A sample contains 7.77 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 = 7.77 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 4005 mL to 4.005 L.
3. Compute M = 1.02 / 4.005.
Final: {"answer": 0.2547, "unit": "mol/L"}

Answer: 0.2547

Prompt: A solution contains 1.02 mol of solute in 4005 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4005 mL to 4.005 L.
Compute M = 1.02 / 4.005.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.1426, "unit": "state_units"}

Answer: 0.1426

Prompt: Use explicit Euler on dy/dt = -0.43 y with y(0)=7, step size h=0.75, for 10 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(2.6)=14.3 and f(4.7)=16.4.
3. The interval width is 2.1.
Final: {"answer": 32.235, "unit": "area_units"}

Answer: 32.235

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1x+11.7 from x=2.6 to x=4.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(2.6)=14.3 and f(4.7)=16.4.
The interval width is 2.1.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.16 and add it to the current value.
Final: {"answer": [-0.194, -0.398, 0.718], "unit": "temperature_units"}

Answer: -0.194

Answer: -0.398

Answer: 0.718

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=1.2; current interior values are [-0.25, -0.75, 0.95]. Use r=0.16. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 22084.0 / 1000.
Final: {"answer": 22.084, "unit": "kg"}

Answer: 22.084

Prompt: Convert 22084 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 22084.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=229 degrees and keep the unit as newtons.
Final: {"answer": [-243.0699, -279.6199], "unit": "N"}

Answer: -243.0699

Answer: -279.6199

Prompt: A vector has magnitude 370.5 N at 229 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=229 degrees and keep the unit as newtons.


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

Answer: inconsistent

Prompt: In student derivation case 50574, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def finite_differences_003760(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_003760"}

Answer: python_code

Prompt: Write a Python function finite_differences_003760(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_003760([5]) == []

assert finite_differences_003760([]) == []


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=0.29 mol and T=605 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 = 24.8 kg and a = 13.35 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 331.08, "unit": "N"}

Answer: 331.08

Prompt: A cart has mass 24.8 kg and measured acceleration 13.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 24.8 kg and a = 13.35 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 = 44.7^2 and multiply by 0.5 * 13.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 13786.821, "unit": "J"}

Answer: 13786.821

Prompt: A body of mass 13.8 kg moves at 44.7 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 44.7^2 and multiply by 0.5 * 13.8.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=62 degrees through the sine of 2 theta.
3. Substitute v=74.2 m/s and g=9.81 m/s^2.
Final: {"answer": 465.2785, "unit": "m"}

Answer: 465.2785

Prompt: A projectile is launched on level ground with no air resistance at speed 74.2 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=74.2 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.31 * 8.314 * 362 / 32.7.
Final: {"answer": 488.7259, "unit": "kPa"}

Answer: 488.7259

Prompt: An ideal gas sample has n=5.31 mol, T=362 K, and V=32.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.31 * 8.314 * 362 / 32.7.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1460 * 3.615 * 13.
Final: {"answer": 68612.7, "unit": "J"}

Answer: 68612.7

Prompt: A 1460 g sample has specific heat 3.615 J/(g*K). How much heat is needed to raise its temperature by 13 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1460 * 3.615 * 13.


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=29.5 V and R=164 ohm.
Final: {"answer": 5.3064, "unit": "W"}

Answer: 5.3064

Prompt: A resistor has resistance 164 ohm and voltage 29.5 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=29.5 V and R=164 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=957 mg, t=322 h, and T_half=72 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 43.116, "unit": "mg"}

Answer: 43.116

Prompt: A radioactive sample starts with 957 mg. Its half-life is 72 hours. How many mg remain after 322 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=957 mg, t=322 h, and T_half=72 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 3650 mL to 3.65 L.
3. Compute M = 4.02 / 3.65.
Final: {"answer": 1.1014, "unit": "mol/L"}

Answer: 1.1014

Prompt: A solution contains 4.02 mol of solute in 3650 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3650 mL to 3.65 L.
Compute M = 4.02 / 3.65.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.77 y, so each step multiplies y by 1 - h*0.77.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.002, "unit": "state_units"}

Answer: 0.002

Prompt: Use explicit Euler on dy/dt = -0.77 y with y(0)=13, step size h=1.6, for 6 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.77 y, so each step multiplies y by 1 - h*0.77.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-3.7)=5.15 and f(-2.7)=7.65.
3. The interval width is 1.
Final: {"answer": 6.4, "unit": "area_units"}

Answer: 6.4

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2.5x+14.4 from x=-3.7 to x=-2.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-3.7)=5.15 and f(-2.7)=7.65.
The interval width is 1.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.18 and add it to the current value.
Final: {"answer": [1.012, -0.074, 0.195], "unit": "temperature_units"}

Answer: 1.012

Answer: -0.074

Answer: 0.195

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.05, right=1.2; current interior values are [1.75, -0.65, 0.15]. 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. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 13762.0 / 1000.
Final: {"answer": 13.762, "unit": "kg"}

Answer: 13.762

Prompt: Convert 13762 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 13762.0 / 1000.


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 instrument manual case 997084, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 55.6 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 = 5.75 kg and a = 10.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 58.9375, "unit": "N"}

Answer: 58.9375

Prompt: A cart has mass 5.75 kg and measured acceleration 10.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 5.75 kg and a = 10.25 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 17.3^2 and multiply by 0.5 * 10.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1526.379, "unit": "J"}

Answer: 1526.379

Prompt: A body of mass 10.2 kg moves at 17.3 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 17.3^2 and multiply by 0.5 * 10.2.
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=37 degrees through the sine of 2 theta.
3. Substitute v=33.1 m/s and g=9.81 m/s^2.
Final: {"answer": 107.3566, "unit": "m"}

Answer: 107.3566

Prompt: A projectile is launched on level ground with no air resistance at speed 33.1 m/s and angle 37 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=37 degrees through the sine of 2 theta.
Substitute v=33.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.93 * 8.314 * 483 / 106.6.
Final: {"answer": 72.7038, "unit": "kPa"}

Answer: 72.7038

Prompt: An ideal gas sample has n=1.93 mol, T=483 K, and V=106.6 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 = 1.93 * 8.314 * 483 / 106.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 605 * 2.93 * 100.
Final: {"answer": 177265.0, "unit": "J"}

Answer: 177265.0

Prompt: A 605 g sample has specific heat 2.93 J/(g*K). How much heat is needed to raise its temperature by 100 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 605 * 2.93 * 100.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=23.1 V and R=59.3 ohm.
Final: {"answer": 8.9985, "unit": "W"}

Answer: 8.9985

Prompt: A resistor has resistance 59.3 ohm and voltage 23.1 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=23.1 V and R=59.3 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.51 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 51.0444, "unit": "g"}

Answer: 51.0444

Prompt: A sample contains 0.51 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 = 0.51 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 295 mL to 0.295 L.
3. Compute M = 4.915 / 0.295.
Final: {"answer": 16.661, "unit": "mol/L"}

Answer: 16.661

Prompt: A solution contains 4.915 mol of solute in 295 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 295 mL to 0.295 L.
Compute M = 4.915 / 0.295.