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

```python
import math

def unit_vector_005236(x, y):
    norm = math.hypot(x, y)
    if norm == 0:
        raise ValueError('zero vector has no direction')
    return (x / norm, y / norm)
```
Final: {"answer": "python_code", "function": "unit_vector_005236"}

Answer: python_code

Prompt: Write a Python function unit_vector_005236(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.

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

try:
    unit_vector_005236(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-1.1)=-20.41 and f(6.5)=3.15.
3. The interval width is 7.6.
Final: {"answer": -65.588, "unit": "area_units"}

Answer: -65.588

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.1x+-17 from x=-1.1 to x=6.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-1.1)=-20.41 and f(6.5)=3.15.
The interval width is 7.6.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 6.4 kg and a = 7.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 48.96, "unit": "N"}

Answer: 48.96

Prompt: A cart has mass 6.4 kg and measured acceleration 7.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 6.4 kg and a = 7.65 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 60 mL to 0.06 L.
3. Compute M = 2.125 / 0.06.
Final: {"answer": 35.4167, "unit": "mol/L"}

Answer: 35.4167

Prompt: A solution contains 2.125 mol of solute in 60 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 60 mL to 0.06 L.
Compute M = 2.125 / 0.06.


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 2843 items and budget 37655, 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. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3490 mL to 3.49 L.
3. Compute M = 1.34 / 3.49.
Final: {"answer": 0.384, "unit": "mol/L"}

Answer: 0.384

Prompt: A solution contains 1.34 mol of solute in 3490 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3490 mL to 3.49 L.
Compute M = 1.34 / 3.49.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.28 and add it to the current value.
Final: {"answer": [0.918, 0.678, 0.512], "unit": "temperature_units"}

Answer: 0.918

Answer: 0.678

Answer: 0.512

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.1, right=0.85; current interior values are [2.5, -0.75, 1.1]. Use r=0.28. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 238.0 + 273.15.
Final: {"answer": 511.15, "unit": "K"}

Answer: 511.15

Prompt: Convert 238 degC to K. Return the converted value with unit.

Kelvin equals Celsius plus 273.15.
Apply the conversion factor directly to the given value.
Compute 238.0 + 273.15.


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_005326(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_005326"}

Answer: python_code

Prompt: Write a Python function running_total_005326(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. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=233.5 V and R=178 ohm.
Final: {"answer": 306.3048, "unit": "W"}

Answer: 306.3048

Prompt: A resistor has resistance 178 ohm and voltage 233.5 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=233.5 V and R=178 ohm.


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

```python
def normalize_005344(values):
    total = sum(values)
    if total == 0:
        raise ValueError('cannot normalize zero-sum values')
    return [v / total for v in values]
```
Final: {"answer": "python_code", "function": "normalize_005344"}

Answer: python_code

Prompt: Write a Python function normalize_005344(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.

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

out = normalize_005344([2, 3, 5]); assert len(out) == 3

try:
    normalize_005344([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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=151.1 V and R=107.2 ohm.
Final: {"answer": 212.9777, "unit": "W"}

Answer: 212.9777

Prompt: A resistor has resistance 107.2 ohm and voltage 151.1 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=151.1 V and R=107.2 ohm.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 34718.0 / 1000.
Final: {"answer": 34.718, "unit": "kg"}

Answer: 34.718

Prompt: Convert 34718 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 34718.0 / 1000.


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 routing scoring problem with 1257 items and budget 66105, 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 Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1140 * 1.175 * 35.
Final: {"answer": 46882.5, "unit": "J"}

Answer: 46882.5

Prompt: A 1140 g sample has specific heat 1.175 J/(g*K). How much heat is needed to raise its temperature by 35 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1140 * 1.175 * 35.


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_005416(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_005416"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_005416(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_005416([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_005416([1, 2], [1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1180 * 2.865 * 2.
Final: {"answer": 6761.4, "unit": "J"}

Answer: 6761.4

Prompt: A 1180 g sample has specific heat 2.865 J/(g*K). How much heat is needed to raise its temperature by 2 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1180 * 2.865 * 2.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4925.0 / 100.
Final: {"answer": 49.25, "unit": "m"}

Answer: 49.25

Prompt: Convert 4925 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 4925.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=251 degrees and keep the unit as newtons.
Final: {"answer": [-27.9989, -81.3146], "unit": "N"}

Answer: -27.9989

Answer: -81.3146

Prompt: A vector has magnitude 86 N at 251 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=251 degrees and keep the unit as newtons.

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


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [1.3, 15.5], "unit": "dimensionless"}

Answer: 1.3

Answer: 15.5

Prompt: A line passes through points (-17.5, -7.25) and (-5.5, 8.35). 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. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 39^2 and multiply by 0.5 * 26.9.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 20457.45, "unit": "J"}

Answer: 20457.45

Prompt: A body of mass 26.9 kg moves at 39 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 39^2 and multiply by 0.5 * 26.9.
The unit kg*m^2/s^2 is one joule.


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=94.5 V and R=49.3 ohm.
Final: {"answer": 181.141, "unit": "W"}

Answer: 181.141

Prompt: A resistor has resistance 49.3 ohm and voltage 94.5 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=94.5 V and R=49.3 ohm.


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 817496, 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. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.09 y, so each step multiplies y by 1 - h*0.09.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 54.4543, "unit": "state_units"}

Answer: 54.4543

Prompt: Use explicit Euler on dy/dt = -0.09 y with y(0)=79, 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) = -0.09 y, so each step multiplies y by 1 - h*0.09.
Apply that update for 9 steps and round the final state.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=254 degrees and keep the unit as newtons.
Final: {"answer": [-120.867, -421.5133], "unit": "N"}

Answer: -120.867

Answer: -421.5133

Prompt: A vector has magnitude 438.5 N at 254 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=254 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.26 and add it to the current value.
Final: {"answer": [0.455, -0.111, -0.847], "unit": "temperature_units"}

Answer: 0.455

Answer: -0.111

Answer: -0.847

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=1.8, right=-0.9; current interior values are [-0.65, 1.15, -1.9]. Use r=0.26. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.26 and add it to the current value.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=357 mg, t=306.5 h, and T_half=67 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 14.9819, "unit": "mg"}

Answer: 14.9819

Prompt: A radioactive sample starts with 357 mg. Its half-life is 67 hours. How many mg remain after 306.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=357 mg, t=306.5 h, and T_half=67 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.38 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 236.7738, "unit": "g"}

Answer: 236.7738

Prompt: A sample contains 5.38 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.38 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


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": [-1.1, -14.0], "unit": "dimensionless"}

Answer: -1.1

Answer: -14.0

Prompt: A line passes through points (13.5, -28.85) and (15.5, -31.05). 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. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 810 * 1.845 * 23.
Final: {"answer": 34372.35, "unit": "J"}

Answer: 34372.35

Prompt: A 810 g sample has specific heat 1.845 J/(g*K). How much heat is needed to raise its temperature by 23 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 810 * 1.845 * 23.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.25 y, so each step multiplies y by 1 - h*0.25.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 0.3466, "unit": "state_units"}

Answer: 0.3466

Prompt: Use explicit Euler on dy/dt = -0.25 y with y(0)=17.5, step size h=1.55, 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) = -0.25 y, so each step multiplies y by 1 - h*0.25.
Apply that update for 8 steps and round the final state.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1510 * 3.955 * 32.
Final: {"answer": 191105.6, "unit": "J"}

Answer: 191105.6

Prompt: A 1510 g sample has specific heat 3.955 J/(g*K). How much heat is needed to raise its temperature by 32 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1510 * 3.955 * 32.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=509.5 mg, t=105.5 h, and T_half=41.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 87.4732, "unit": "mg"}

Answer: 87.4732

Prompt: A radioactive sample starts with 509.5 mg. Its half-life is 41.5 hours. How many mg remain after 105.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=509.5 mg, t=105.5 h, and T_half=41.5 h.
The remaining amount has the same mass unit as the initial amount.


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 = 1.28 * 8.314 * 464 / 21.9.
Final: {"answer": 225.4726, "unit": "kPa"}

Answer: 225.4726

Prompt: An ideal gas sample has n=1.28 mol, T=464 K, and V=21.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.28 * 8.314 * 464 / 21.9.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=9 degrees through the sine of 2 theta.
3. Substitute v=35.3 m/s and g=9.81 m/s^2.
Final: {"answer": 39.2521, "unit": "m"}

Answer: 39.2521

Prompt: A projectile is launched on level ground with no air resistance at speed 35.3 m/s and angle 9 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=9 degrees through the sine of 2 theta.
Substitute v=35.3 m/s and g=9.81 m/s^2.

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


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_005650(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_005650"}

Answer: python_code

Prompt: Write a Python function weighted_sum_005650(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_005650([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 26.85^2 and multiply by 0.5 * 5.65.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2036.6061, "unit": "J"}

Answer: 2036.6061

Prompt: A body of mass 5.65 kg moves at 26.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 26.85^2 and multiply by 0.5 * 5.65.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(4.6)=45.28 and f(8.5)=67.9.
3. The interval width is 3.9.
Final: {"answer": 220.701, "unit": "area_units"}

Answer: 220.701

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5.8x+18.6 from x=4.6 to x=8.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.6)=45.28 and f(8.5)=67.9.
The interval width is 3.9.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=77 degrees and keep the unit as newtons.
Final: {"answer": [105.1646, 455.518], "unit": "N"}

Answer: 105.1646

Answer: 455.518

Prompt: A vector has magnitude 467.5 N at 77 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=77 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [6.8, -2.25], "unit": "dimensionless"}

Answer: 6.8

Answer: -2.25

Prompt: A line passes through points (-3.25, -24.35) and (-2.5, -19.25). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.34 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 58.9734, "unit": "g"}

Answer: 58.9734

Prompt: A sample contains 1.34 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.34 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 1805 mL to 1.805 L.
3. Compute M = 2.165 / 1.805.
Final: {"answer": 1.1994, "unit": "mol/L"}

Answer: 1.1994

Prompt: A solution contains 2.165 mol of solute in 1805 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1805 mL to 1.805 L.
Compute M = 2.165 / 1.805.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=335 degrees and keep the unit as newtons.
Final: {"answer": [372.0393, -173.4848], "unit": "N"}

Answer: 372.0393

Answer: -173.4848

Prompt: A vector has magnitude 410.5 N at 335 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=335 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-8.85, -8.75], "unit": "dimensionless"}

Answer: -8.85

Answer: -8.75

Prompt: A line passes through points (1.5, -22.025) and (6.5, -66.275). 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. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=83 degrees through the sine of 2 theta.
3. Substitute v=26.9 m/s and g=9.81 m/s^2.
Final: {"answer": 17.8448, "unit": "m"}

Answer: 17.8448

Prompt: A projectile is launched on level ground with no air resistance at speed 26.9 m/s and angle 83 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=83 degrees through the sine of 2 theta.
Substitute v=26.9 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1838.5 / 100.
Final: {"answer": 18.385, "unit": "m"}

Answer: 18.385

Prompt: Convert 1838.5 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 1838.5 / 100.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3630 mL to 3.63 L.
3. Compute M = 2.655 / 3.63.
Final: {"answer": 0.7314, "unit": "mol/L"}

Answer: 0.7314

Prompt: A solution contains 2.655 mol of solute in 3630 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3630 mL to 3.63 L.
Compute M = 2.655 / 3.63.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=366.5 mg, t=105 h, and T_half=78 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 144.1588, "unit": "mg"}

Answer: 144.1588

Prompt: A radioactive sample starts with 366.5 mg. Its half-life is 78 hours. How many mg remain after 105 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=366.5 mg, t=105 h, and T_half=78 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.28 and add it to the current value.
Final: {"answer": [-1.544, -0.376, 1.27], "unit": "temperature_units"}

Answer: -1.544

Answer: -0.376

Answer: 1.27

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=-1.85, right=2.7; current interior values are [-1.95, -0.6, 1.55]. Use r=0.28. Return the next interior vector.

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


Response:
Reasoning:
1. 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=0.12 and interior values [1.45, -0.45, 2.3], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. 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=0.34 and add it to the current value.
Final: {"answer": [0.009, -0.14, 0.719], "unit": "temperature_units"}

Answer: 0.009

Answer: -0.14

Answer: 0.719

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.95, right=2.25; current interior values are [-0.45, -1.5, 1.45]. Use r=0.34. 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=0.34 and add it to the current value.


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=111.5 V and R=161.4 ohm.
Final: {"answer": 77.0276, "unit": "W"}

Answer: 77.0276

Prompt: A resistor has resistance 161.4 ohm and voltage 111.5 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=111.5 V and R=161.4 ohm.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.62 y, so each step multiplies y by 1 - h*0.62.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 0.3188, "unit": "state_units"}

Answer: 0.3188

Prompt: Use explicit Euler on dy/dt = -0.62 y with y(0)=12, step size h=1.35, 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) = -0.62 y, so each step multiplies y by 1 - h*0.62.
Apply that update for 2 steps and round the final state.


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

```python
def normalize_005776(values):
    total = sum(values)
    if total == 0:
        raise ValueError('cannot normalize zero-sum values')
    return [v / total for v in values]
```
Final: {"answer": "python_code", "function": "normalize_005776"}

Answer: python_code

Prompt: Write a Python function normalize_005776(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.

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

out = normalize_005776([2, 3, 5]); assert len(out) == 3

try:
    normalize_005776([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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 = 4.19 * 8.314 * 300 / 63.3.
Final: {"answer": 165.0979, "unit": "kPa"}

Answer: 165.0979

Prompt: An ideal gas sample has n=4.19 mol, T=300 K, and V=63.3 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 = 4.19 * 8.314 * 300 / 63.3.


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

Answer: inconsistent

Prompt: In model card equation case 541130, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 10952.0 / 1000.
Final: {"answer": 10.952, "unit": "kg"}

Answer: 10.952

Prompt: Convert 10952 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 10952.0 / 1000.


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

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each field clinical record from batch 286382 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 26.85^2 and multiply by 0.5 * 0.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 108.1384, "unit": "J"}

Answer: 108.1384

Prompt: A body of mass 0.3 kg moves at 26.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 26.85^2 and multiply by 0.5 * 0.3.
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 = 690 * 4.24 * 70.
Final: {"answer": 204792.0, "unit": "J"}

Answer: 204792.0

Prompt: A 690 g sample has specific heat 4.24 J/(g*K). How much heat is needed to raise its temperature by 70 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 690 * 4.24 * 70.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 330 mL to 0.33 L.
3. Compute M = 1.035 / 0.33.
Final: {"answer": 3.1364, "unit": "mol/L"}

Answer: 3.1364

Prompt: A solution contains 1.035 mol of solute in 330 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 330 mL to 0.33 L.
Compute M = 1.035 / 0.33.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=5 degrees through the sine of 2 theta.
3. Substitute v=76.3 m/s and g=9.81 m/s^2.
Final: {"answer": 103.0505, "unit": "m"}

Answer: 103.0505

Prompt: A projectile is launched on level ground with no air resistance at speed 76.3 m/s and angle 5 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=5 degrees through the sine of 2 theta.
Substitute v=76.3 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3205 mL to 3.205 L.
3. Compute M = 3.925 / 3.205.
Final: {"answer": 1.2246, "unit": "mol/L"}

Answer: 1.2246

Prompt: A solution contains 3.925 mol of solute in 3205 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3205 mL to 3.205 L.
Compute M = 3.925 / 3.205.


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=4.84 mol and T=504 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 = 18.3 kg and a = 12.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 229.665, "unit": "N"}

Answer: 229.665

Prompt: A cart has mass 18.3 kg and measured acceleration 12.55 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 = 18.3 kg and a = 12.55 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 211.0 / 100.
Final: {"answer": 2.11, "unit": "m"}

Answer: 2.11

Prompt: Convert 211 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 211.0 / 100.


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

Answer: inconsistent

Prompt: In quality-control check case 534652, 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. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=54 degrees through the sine of 2 theta.
3. Substitute v=51.9 m/s and g=9.81 m/s^2.
Final: {"answer": 261.1392, "unit": "m"}

Answer: 261.1392

Prompt: A projectile is launched on level ground with no air resistance at speed 51.9 m/s and angle 54 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=54 degrees through the sine of 2 theta.
Substitute v=51.9 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 = 1670 * 3.855 * 21.
Final: {"answer": 135194.85, "unit": "J"}

Answer: 135194.85

Prompt: A 1670 g sample has specific heat 3.855 J/(g*K). How much heat is needed to raise its temperature by 21 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1670 * 3.855 * 21.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 14^2 and multiply by 0.5 * 8.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 867.3, "unit": "J"}

Answer: 867.3

Prompt: A body of mass 8.85 kg moves at 14 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 14^2 and multiply by 0.5 * 8.85.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.48 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 26.6622, "unit": "g"}

Answer: 26.6622

Prompt: A sample contains 1.48 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 = 1.48 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(4.5)=-35.5 and f(13.9)=-106.94.
3. The interval width is 9.4.
Final: {"answer": -669.468, "unit": "area_units"}

Answer: -669.468

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.6x+-1.3 from x=4.5 to x=13.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.5)=-35.5 and f(13.9)=-106.94.
The interval width is 9.4.


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=0.98 mol and T=285 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. Compare the dimensions on both sides of the equation.
2. amount times volume is not concentration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In model card equation case 176354, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1300 * 4.365 * 68.
Final: {"answer": 385866.0, "unit": "J"}

Answer: 385866.0

Prompt: A 1300 g sample has specific heat 4.365 J/(g*K). How much heat is needed to raise its temperature by 68 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1300 * 4.365 * 68.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 4.95^2 and multiply by 0.5 * 1.65.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 20.2146, "unit": "J"}

Answer: 20.2146

Prompt: A body of mass 1.65 kg moves at 4.95 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 4.95^2 and multiply by 0.5 * 1.65.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 760 mL to 0.76 L.
3. Compute M = 2.805 / 0.76.
Final: {"answer": 3.6908, "unit": "mol/L"}

Answer: 3.6908

Prompt: A solution contains 2.805 mol of solute in 760 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 760 mL to 0.76 L.
Compute M = 2.805 / 0.76.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 2.5708, "unit": "state_units"}

Answer: 2.5708

Prompt: Use explicit Euler on dy/dt = -0.47 y with y(0)=69, step size h=0.55, for 11 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.
Apply that update for 11 steps and round the final state.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 34.15^2 and multiply by 0.5 * 23.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 13615.6477, "unit": "J"}

Answer: 13615.6477

Prompt: A body of mass 23.35 kg moves at 34.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 34.15^2 and multiply by 0.5 * 23.35.
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=85 degrees through the sine of 2 theta.
3. Substitute v=18.4 m/s and g=9.81 m/s^2.
Final: {"answer": 5.9929, "unit": "m"}

Answer: 5.9929

Prompt: A projectile is launched on level ground with no air resistance at speed 18.4 m/s and angle 85 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=85 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 = 2.82 * 8.314 * 394 / 50.2.
Final: {"answer": 184.0143, "unit": "kPa"}

Answer: 184.0143

Prompt: An ideal gas sample has n=2.82 mol, T=394 K, and V=50.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.82 * 8.314 * 394 / 50.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1630 * 4.55 * 45.
Final: {"answer": 333742.5, "unit": "J"}

Answer: 333742.5

Prompt: A 1630 g sample has specific heat 4.55 J/(g*K). How much heat is needed to raise its temperature by 45 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1630 * 4.55 * 45.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=226 degrees and keep the unit as newtons.
Final: {"answer": [-92.0422, -95.3125], "unit": "N"}

Answer: -92.0422

Answer: -95.3125

Prompt: A vector has magnitude 132.5 N at 226 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=226 degrees and keep the unit as newtons.


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

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=37.5 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 = 23.6 kg and a = 7.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 171.1, "unit": "N"}

Answer: 171.1

Prompt: A cart has mass 23.6 kg and measured acceleration 7.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 23.6 kg and a = 7.25 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-7.8)=-18.38 and f(-3)=-15.5.
3. The interval width is 4.8.
Final: {"answer": -81.312, "unit": "area_units"}

Answer: -81.312

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.6x+-13.7 from x=-7.8 to x=-3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.8)=-18.38 and f(-3)=-15.5.
The interval width is 4.8.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2515 mL to 2.515 L.
3. Compute M = 4.8 / 2.515.
Final: {"answer": 1.9085, "unit": "mol/L"}

Answer: 1.9085

Prompt: A solution contains 4.8 mol of solute in 2515 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2515 mL to 2.515 L.
Compute M = 4.8 / 2.515.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1375 * 4.475 * 32.
Final: {"answer": 196900.0, "unit": "J"}

Answer: 196900.0

Prompt: A 1375 g sample has specific heat 4.475 J/(g*K). How much heat is needed to raise its temperature by 32 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1375 * 4.475 * 32.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 16.1^2 and multiply by 0.5 * 23.95.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3104.0398, "unit": "J"}

Answer: 3104.0398

Prompt: A body of mass 23.95 kg moves at 16.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 16.1^2 and multiply by 0.5 * 23.95.
The unit kg*m^2/s^2 is one joule.


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": [-0.15, 10.25], "unit": "dimensionless"}

Answer: -0.15

Answer: 10.25

Prompt: A line passes through points (-15.5, 12.575) and (-9.25, 11.6375). 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. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 24.55^2 and multiply by 0.5 * 5.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1506.7562, "unit": "J"}

Answer: 1506.7562

Prompt: A body of mass 5 kg moves at 24.55 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 24.55^2 and multiply by 0.5 * 5.
The unit kg*m^2/s^2 is one joule.


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

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=6.5 and h=1.6, 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 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 = 2.33 * 8.314 * 375 / 74.2.
Final: {"answer": 97.9024, "unit": "kPa"}

Answer: 97.9024

Prompt: An ideal gas sample has n=2.33 mol, T=375 K, and V=74.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.33 * 8.314 * 375 / 74.2.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=75 degrees and keep the unit as newtons.
Final: {"answer": [16.9526, 63.2681], "unit": "N"}

Answer: 16.9526

Answer: 63.2681

Prompt: A vector has magnitude 65.5 N at 75 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=75 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=743 mg, t=250.5 h, and T_half=120 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 174.819, "unit": "mg"}

Answer: 174.819

Prompt: A radioactive sample starts with 743 mg. Its half-life is 120 hours. How many mg remain after 250.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=743 mg, t=250.5 h, and T_half=120 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(-9.3)=76.71 and f(-3.5)=32.05.
3. The interval width is 5.8.
Final: {"answer": 315.404, "unit": "area_units"}

Answer: 315.404

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.7x+5.1 from x=-9.3 to x=-3.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.3)=76.71 and f(-3.5)=32.05.
The interval width is 5.8.


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_006280(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_006280"}

Answer: python_code

Prompt: Write a Python function weighted_sum_006280(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_006280([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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=154.2 V and R=62.5 ohm.
Final: {"answer": 380.4422, "unit": "W"}

Answer: 380.4422

Prompt: A resistor has resistance 62.5 ohm and voltage 154.2 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=154.2 V and R=62.5 ohm.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.45 y, so each step multiplies y by 1 - h*0.45.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.0004, "unit": "state_units"}

Answer: 0.0004

Prompt: Use explicit Euler on dy/dt = -0.45 y with y(0)=65.5, step size h=1.4, for 12 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.45 y, so each step multiplies y by 1 - h*0.45.
Apply that update for 12 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=0.06 and add it to the current value.
Final: {"answer": [1.207, -0.845, 2.344], "unit": "temperature_units"}

Answer: 1.207

Answer: -0.845

Answer: 2.344

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.1, right=-0.75; current interior values are [1.45, -1.25, 2.8]. Use r=0.06. Return the next interior vector.

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


Response:
Reasoning:
1. 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 lab notebook case 763477, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. Use 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 = 2.49 * 8.314 * 256 / 3.7.
Final: {"answer": 1432.3449, "unit": "kPa"}

Answer: 1432.3449

Prompt: An ideal gas sample has n=2.49 mol, T=256 K, and V=3.7 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 = 2.49 * 8.314 * 256 / 3.7.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 2956.0 / 100.
Final: {"answer": 29.56, "unit": "m"}

Answer: 29.56

Prompt: Convert 2956 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 2956.0 / 100.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 19.4 kg and a = 11.9 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 230.86, "unit": "N"}

Answer: 230.86

Prompt: A cart has mass 19.4 kg and measured acceleration 11.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 19.4 kg and a = 11.9 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 20.75 kg and a = 1.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 32.1625, "unit": "N"}

Answer: 32.1625

Prompt: A cart has mass 20.75 kg and measured acceleration 1.55 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 = 20.75 kg and a = 1.55 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 15.65 kg and a = 6.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 97.8125, "unit": "N"}

Answer: 97.8125

Prompt: A cart has mass 15.65 kg and measured acceleration 6.25 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 = 15.65 kg and a = 6.25 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 = 21.4^2 and multiply by 0.5 * 23.1.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5289.438, "unit": "J"}

Answer: 5289.438

Prompt: A body of mass 23.1 kg moves at 21.4 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 21.4^2 and multiply by 0.5 * 23.1.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.28 and add it to the current value.
Final: {"answer": [0.444, 0.81, 1.374], "unit": "temperature_units"}

Answer: 0.444

Answer: 0.81

Answer: 1.374

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.45, right=0.45; current interior values are [0.15, -0.1, 2.9]. Use r=0.28. Return the next interior vector.

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


Response:
Reasoning:
1. 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_006388(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_006388"}

Answer: python_code

Prompt: Write a Python function finite_differences_006388(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_006388([5]) == []

assert finite_differences_006388([]) == []


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

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 57.4 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 = 9.6 kg and a = 5.05 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 48.48, "unit": "N"}

Answer: 48.48

Prompt: A cart has mass 9.6 kg and measured acceleration 5.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 9.6 kg and a = 5.05 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 34.2^2 and multiply by 0.5 * 29.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 16989.021, "unit": "J"}

Answer: 16989.021

Prompt: A body of mass 29.05 kg moves at 34.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 34.2^2 and multiply by 0.5 * 29.05.
The unit kg*m^2/s^2 is one joule.


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 sensor calibration case 279036, 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. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=539 mg, t=81 h, and T_half=24 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 51.9532, "unit": "mg"}

Answer: 51.9532

Prompt: A radioactive sample starts with 539 mg. Its half-life is 24 hours. How many mg remain after 81 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=539 mg, t=81 h, and T_half=24 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3904.5 / 100.
Final: {"answer": 39.045, "unit": "m"}

Answer: 39.045

Prompt: Convert 3904.5 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 3904.5 / 100.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 39^2 and multiply by 0.5 * 12.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 9164.025, "unit": "J"}

Answer: 9164.025

Prompt: A body of mass 12.05 kg moves at 39 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 39^2 and multiply by 0.5 * 12.05.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=968 mg, t=292 h, and T_half=43 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 8.7432, "unit": "mg"}

Answer: 8.7432

Prompt: A radioactive sample starts with 968 mg. Its half-life is 43 hours. How many mg remain after 292 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=968 mg, t=292 h, and T_half=43 h.
The remaining amount has the same mass unit as the initial amount.


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": [-1.55, -10.75], "unit": "dimensionless"}

Answer: -1.55

Answer: -10.75

Prompt: A line passes through points (9.25, -25.0875) and (23.5, -47.175). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.35 y, so each step multiplies y by 1 - h*0.35.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 2.5467, "unit": "state_units"}

Answer: 2.5467

Prompt: Use explicit Euler on dy/dt = -0.35 y with y(0)=53.5, 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) = -0.35 y, so each step multiplies y by 1 - h*0.35.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 12.75 kg and a = 15.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 199.5375, "unit": "N"}

Answer: 199.5375

Prompt: A cart has mass 12.75 kg and measured acceleration 15.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 12.75 kg and a = 15.65 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=80 degrees through the sine of 2 theta.
3. Substitute v=50.5 m/s and g=9.81 m/s^2.
Final: {"answer": 88.913, "unit": "m"}

Answer: 88.913

Prompt: A projectile is launched on level ground with no air resistance at speed 50.5 m/s and angle 80 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=80 degrees through the sine of 2 theta.
Substitute v=50.5 m/s and g=9.81 m/s^2.


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

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid billing clinical records in release 788933, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use 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 = 1.86 * 8.314 * 494 / 68.7.
Final: {"answer": 111.197, "unit": "kPa"}

Answer: 111.197

Prompt: An ideal gas sample has n=1.86 mol, T=494 K, and V=68.7 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 = 1.86 * 8.314 * 494 / 68.7.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=141.5 mg, t=157.5 h, and T_half=13.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0435, "unit": "mg"}

Answer: 0.0435

Prompt: A radioactive sample starts with 141.5 mg. Its half-life is 13.5 hours. How many mg remain after 157.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=141.5 mg, t=157.5 h, and T_half=13.5 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(7.6)=-24.82 and f(17.2)=-69.94.
3. The interval width is 9.6.
Final: {"answer": -454.848, "unit": "area_units"}

Answer: -454.848

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.7x+10.9 from x=7.6 to x=17.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7.6)=-24.82 and f(17.2)=-69.94.
The interval width is 9.6.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=59 degrees through the sine of 2 theta.
3. Substitute v=27.7 m/s and g=9.81 m/s^2.
Final: {"answer": 69.0598, "unit": "m"}

Answer: 69.0598

Prompt: A projectile is launched on level ground with no air resistance at speed 27.7 m/s and angle 59 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=59 degrees through the sine of 2 theta.
Substitute v=27.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=215.2 V and R=15.9 ohm.
Final: {"answer": 2912.644, "unit": "W"}

Answer: 2912.644

Prompt: A resistor has resistance 15.9 ohm and voltage 215.2 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=215.2 V and R=15.9 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.75 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 75.0653, "unit": "g"}

Answer: 75.0653

Prompt: A sample contains 0.75 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 = 0.75 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.07 y, so each step multiplies y by 1 - h*0.07.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 11.7048, "unit": "state_units"}

Answer: 11.7048

Prompt: Use explicit Euler on dy/dt = -0.07 y with y(0)=15, step size h=0.35, 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) = -0.07 y, so each step multiplies y by 1 - h*0.07.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6.8)=-5.1 and f(1.6)=20.1.
3. The interval width is 8.4.
Final: {"answer": 63.0, "unit": "area_units"}

Answer: 63.0

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3x+15.3 from x=-6.8 to x=1.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.8)=-5.1 and f(1.6)=20.1.
The interval width is 8.4.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=147 degrees and keep the unit as newtons.
Final: {"answer": [-76.319, 49.5622], "unit": "N"}

Answer: -76.319

Answer: 49.5622

Prompt: A vector has magnitude 91 N at 147 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=147 degrees and keep the unit as newtons.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=46 degrees through the sine of 2 theta.
3. Substitute v=57.4 m/s and g=9.81 m/s^2.
Final: {"answer": 335.6527, "unit": "m"}

Answer: 335.6527

Prompt: A projectile is launched on level ground with no air resistance at speed 57.4 m/s and angle 46 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=46 degrees through the sine of 2 theta.
Substitute v=57.4 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.91 y, so each step multiplies y by 1 - h*0.91.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 1.0795, "unit": "state_units"}

Answer: 1.0795

Prompt: Use explicit Euler on dy/dt = -0.91 y with y(0)=3, step size h=1.95, for 4 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.91 y, so each step multiplies y by 1 - h*0.91.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [1.05, 24.5], "unit": "dimensionless"}

Answer: 1.05

Answer: 24.5

Prompt: A line passes through points (-0.25, 24.2375) and (3.5, 28.175). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In simulation spec case 318074, 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. 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 77.2 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 1.35^2 and multiply by 0.5 * 25.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 23.0546, "unit": "J"}

Answer: 23.0546

Prompt: A body of mass 25.3 kg moves at 1.35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 1.35^2 and multiply by 0.5 * 25.3.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=642 mg, t=303.5 h, and T_half=55 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 14.0087, "unit": "mg"}

Answer: 14.0087

Prompt: A radioactive sample starts with 642 mg. Its half-life is 55 hours. How many mg remain after 303.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=642 mg, t=303.5 h, and T_half=55 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) = -0.57 y, so each step multiplies y by 1 - h*0.57.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 0.0609, "unit": "state_units"}

Answer: 0.0609

Prompt: Use explicit Euler on dy/dt = -0.57 y with y(0)=31, step size h=1.25, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.57 y, so each step multiplies y by 1 - h*0.57.
Apply that update for 5 steps and round the final state.


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 simulation spec case 558238, 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. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=52.7 V and R=162.9 ohm.
Final: {"answer": 17.049, "unit": "W"}

Answer: 17.049

Prompt: A resistor has resistance 162.9 ohm and voltage 52.7 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=52.7 V and R=162.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=518 mg, t=328 h, and T_half=80.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 30.7449, "unit": "mg"}

Answer: 30.7449

Prompt: A radioactive sample starts with 518 mg. Its half-life is 80.5 hours. How many mg remain after 328 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=518 mg, t=328 h, and T_half=80.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 380 * 4.5 * 72.
Final: {"answer": 123120.0, "unit": "J"}

Answer: 123120.0

Prompt: A 380 g sample has specific heat 4.5 J/(g*K). How much heat is needed to raise its temperature by 72 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 380 * 4.5 * 72.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=664 mg, t=329 h, and T_half=83 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 42.5529, "unit": "mg"}

Answer: 42.5529

Prompt: A radioactive sample starts with 664 mg. Its half-life is 83 hours. How many mg remain after 329 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=664 mg, t=329 h, and T_half=83 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(6.7)=24.08 and f(9)=29.6.
3. The interval width is 2.3.
Final: {"answer": 61.732, "unit": "area_units"}

Answer: 61.732

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2.4x+8 from x=6.7 to x=9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.7)=24.08 and f(9)=29.6.
The interval width is 2.3.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-6.2, 12.5], "unit": "dimensionless"}

Answer: -6.2

Answer: 12.5

Prompt: A line passes through points (9.25, -44.85) and (16, -86.7). 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. Use Newton's second law F = m a.
2. Substitute m = 18.5 kg and a = 11.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 208.125, "unit": "N"}

Answer: 208.125

Prompt: A cart has mass 18.5 kg and measured acceleration 11.25 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 = 18.5 kg and a = 11.25 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=786.5 mg, t=180 h, and T_half=41.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 38.9069, "unit": "mg"}

Answer: 38.9069

Prompt: A radioactive sample starts with 786.5 mg. Its half-life is 41.5 hours. How many mg remain after 180 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=786.5 mg, t=180 h, and T_half=41.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3115.0 / 100.
Final: {"answer": 31.15, "unit": "m"}

Answer: 31.15

Prompt: Convert 3115 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 3115.0 / 100.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 2.5^2 and multiply by 0.5 * 18.1.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 56.5625, "unit": "J"}

Answer: 56.5625

Prompt: A body of mass 18.1 kg moves at 2.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 2.5^2 and multiply by 0.5 * 18.1.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": -0.0189, "unit": "state_units"}

Answer: -0.0189

Prompt: Use explicit Euler on dy/dt = -0.78 y with y(0)=58, step size h=1.9, for 11 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.
Apply that update for 11 steps and round the final state.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.97 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1075.5313, "unit": "g"}

Answer: 1075.5313

Prompt: A sample contains 5.97 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 = 5.97 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1267.5 / 100.
Final: {"answer": 12.675, "unit": "m"}

Answer: 12.675

Prompt: Convert 1267.5 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 1267.5 / 100.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 205.5 + 273.15.
Final: {"answer": 478.65, "unit": "K"}

Answer: 478.65

Prompt: Convert 205.5 degC to K. Return the converted value with unit.

Kelvin equals Celsius plus 273.15.
Apply the conversion factor directly to the given value.
Compute 205.5 + 273.15.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.61 y, so each step multiplies y by 1 - h*0.61.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 28.0391, "unit": "state_units"}

Answer: 28.0391

Prompt: Use explicit Euler on dy/dt = -0.61 y with y(0)=63.5, step size h=0.55, 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) = -0.61 y, so each step multiplies y by 1 - h*0.61.
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=0.1 and add it to the current value.
Final: {"answer": [-1.04, 0.78, -1.035], "unit": "temperature_units"}

Answer: -1.04

Answer: 0.78

Answer: -1.035

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=-0.15, right=0.7; current interior values are [-1.45, 1.35, -1.55]. Use r=0.1. Return the next interior vector.

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


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=217.9 V and R=27.4 ohm.
Final: {"answer": 1732.8617, "unit": "W"}

Answer: 1732.8617

Prompt: A resistor has resistance 27.4 ohm and voltage 217.9 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=217.9 V and R=27.4 ohm.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.38 and add it to the current value.
Final: {"answer": [0.466, 0.934, 1.432], "unit": "temperature_units"}

Answer: 0.466

Answer: 0.934

Answer: 1.432

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.65, right=1.65; current interior values are [1.15, 2.15, -0.05]. Use r=0.38. Return the next interior vector.

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


Response:
Reasoning:
1. 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 student derivation case 631831, 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. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=116.8 V and R=4.5 ohm.
Final: {"answer": 3031.6089, "unit": "W"}

Answer: 3031.6089

Prompt: A resistor has resistance 4.5 ohm and voltage 116.8 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=116.8 V and R=4.5 ohm.


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 1032 items and budget 8660, 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 Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 130 * 4.45 * 55.
Final: {"answer": 31817.5, "unit": "J"}

Answer: 31817.5

Prompt: A 130 g sample has specific heat 4.45 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 = 130 * 4.45 * 55.


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_006874(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_006874"}

Answer: python_code

Prompt: Write a Python function safe_mean_006874(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_006874([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=46 degrees through the sine of 2 theta.
3. Substitute v=68.1 m/s and g=9.81 m/s^2.
Final: {"answer": 472.4551, "unit": "m"}

Answer: 472.4551

Prompt: A projectile is launched on level ground with no air resistance at speed 68.1 m/s and angle 46 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=46 degrees through the sine of 2 theta.
Substitute v=68.1 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 = 2.42 * 8.314 * 497 / 102.0.
Final: {"answer": 98.0351, "unit": "kPa"}

Answer: 98.0351

Prompt: An ideal gas sample has n=2.42 mol, T=497 K, and V=102.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.42 * 8.314 * 497 / 102.0.


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)=69 and h=0.15, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=69 degrees through the sine of 2 theta.
3. Substitute v=52.7 m/s and g=9.81 m/s^2.
Final: {"answer": 189.4363, "unit": "m"}

Answer: 189.4363

Prompt: A projectile is launched on level ground with no air resistance at speed 52.7 m/s and angle 69 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=69 degrees through the sine of 2 theta.
Substitute v=52.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.86 * 8.314 * 443 / 117.8.
Final: {"answer": 183.2171, "unit": "kPa"}

Answer: 183.2171

Prompt: An ideal gas sample has n=5.86 mol, T=443 K, and V=117.8 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 = 5.86 * 8.314 * 443 / 117.8.


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 simulation spec case 46252, 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. 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 1353 items and budget 93415, 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 = 10.9 kg and a = 10.35 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 112.815, "unit": "N"}

Answer: 112.815

Prompt: A cart has mass 10.9 kg and measured acceleration 10.35 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 = 10.9 kg and a = 10.35 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2370 mL to 2.37 L.
3. Compute M = 0.71 / 2.37.
Final: {"answer": 0.2996, "unit": "mol/L"}

Answer: 0.2996

Prompt: A solution contains 0.71 mol of solute in 2370 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2370 mL to 2.37 L.
Compute M = 0.71 / 2.37.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.35 y, so each step multiplies y by 1 - h*0.35.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 9.2197, "unit": "state_units"}

Answer: 9.2197

Prompt: Use explicit Euler on dy/dt = -0.35 y with y(0)=11, step size h=0.05, 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) = -0.35 y, so each step multiplies y by 1 - h*0.35.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.23 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 230.1723, "unit": "g"}

Answer: 230.1723

Prompt: A sample contains 5.23 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.23 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 4015 mL to 4.015 L.
3. Compute M = 0.445 / 4.015.
Final: {"answer": 0.1108, "unit": "mol/L"}

Answer: 0.1108

Prompt: A solution contains 0.445 mol of solute in 4015 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4015 mL to 4.015 L.
Compute M = 0.445 / 4.015.


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

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each mobile invoice record from batch 767726 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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