Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 1.2 kg and a = 8.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 10.38, "unit": "N"}

Answer: 10.38

Prompt: A cart has mass 1.2 kg and measured acceleration 8.65 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 = 1.2 kg and a = 8.65 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 23.35^2 and multiply by 0.5 * 18.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5111.4609, "unit": "J"}

Answer: 5111.4609

Prompt: A body of mass 18.75 kg moves at 23.35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 23.35^2 and multiply by 0.5 * 18.75.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=45 degrees through the sine of 2 theta.
3. Substitute v=10.8 m/s and g=9.81 m/s^2.
Final: {"answer": 11.8899, "unit": "m"}

Answer: 11.8899

Prompt: A projectile is launched on level ground with no air resistance at speed 10.8 m/s and angle 45 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=45 degrees through the sine of 2 theta.
Substitute v=10.8 m/s and g=9.81 m/s^2.

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


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1210 * 2.365 * 10.
Final: {"answer": 28616.5, "unit": "J"}

Answer: 28616.5

Prompt: A 1210 g sample has specific heat 2.365 J/(g*K). How much heat is needed to raise its temperature by 10 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1210 * 2.365 * 10.


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=35 V and R=195.1 ohm.
Final: {"answer": 6.2788, "unit": "W"}

Answer: 6.2788

Prompt: A resistor has resistance 195.1 ohm and voltage 35 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=35 V and R=195.1 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.36 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 236.2053, "unit": "g"}

Answer: 236.2053

Prompt: A sample contains 2.36 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 2.36 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) = -0.78 y, so each step multiplies y by 1 - h*0.78.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 15.6617, "unit": "state_units"}

Answer: 15.6617

Prompt: Use explicit Euler on dy/dt = -0.78 y with y(0)=69, step size h=0.5, for 3 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.
Apply that update for 3 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=0.28 and add it to the current value.
Final: {"answer": [1.566, 1.956, 2.13], "unit": "temperature_units"}

Answer: 1.566

Answer: 1.956

Answer: 2.13

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.45, right=1.5; current interior values are [1.65, 1.55, 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -20.5 + 273.15.
Final: {"answer": 252.65, "unit": "K"}

Answer: 252.65

Prompt: Convert -20.5 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 -20.5 + 273.15.


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 model card equation case 131890, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def weighted_sum_000016(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_000016"}

Answer: python_code

Prompt: Write a Python function weighted_sum_000016(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_000016([1], [1, 2])
    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=34 degrees through the sine of 2 theta.
3. Substitute v=60.7 m/s and g=9.81 m/s^2.
Final: {"answer": 348.2365, "unit": "m"}

Answer: 348.2365

Prompt: A projectile is launched on level ground with no air resistance at speed 60.7 m/s and angle 34 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=34 degrees through the sine of 2 theta.
Substitute v=60.7 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=200.3 V and R=93.4 ohm.
Final: {"answer": 429.5513, "unit": "W"}

Answer: 429.5513

Prompt: A resistor has resistance 93.4 ohm and voltage 200.3 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=200.3 V and R=93.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=789.5 mg, t=296.5 h, and T_half=47.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 10.4302, "unit": "mg"}

Answer: 10.4302

Prompt: A radioactive sample starts with 789.5 mg. Its half-life is 47.5 hours. How many mg remain after 296.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=789.5 mg, t=296.5 h, and T_half=47.5 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.47 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 85.9068, "unit": "g"}

Answer: 85.9068

Prompt: A sample contains 1.47 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.47 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1100 mL to 1.1 L.
3. Compute M = 1.005 / 1.1.
Final: {"answer": 0.9136, "unit": "mol/L"}

Answer: 0.9136

Prompt: A solution contains 1.005 mol of solute in 1100 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1100 mL to 1.1 L.
Compute M = 1.005 / 1.1.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 7.0267, "unit": "state_units"}

Answer: 7.0267

Prompt: Use explicit Euler on dy/dt = -0.08 y with y(0)=9, step size h=0.75, 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) = -0.08 y, so each step multiplies y by 1 - h*0.08.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-7.3)=-33.84 and f(-6.3)=-30.04.
3. The interval width is 1.
Final: {"answer": -31.94, "unit": "area_units"}

Answer: -31.94

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.8x+-6.1 from x=-7.3 to x=-6.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.3)=-33.84 and f(-6.3)=-30.04.
The interval width is 1.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 176.5 + 273.15.
Final: {"answer": 449.65, "unit": "K"}

Answer: 449.65

Prompt: Convert 176.5 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 176.5 + 273.15.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-6.1, -1.75], "unit": "dimensionless"}

Answer: -6.1

Answer: -1.75

Prompt: A line passes through points (-10.5, 62.3) and (1.75, -12.425). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In simulation spec case 463582, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def safe_mean_000034(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_000034"}

Answer: python_code

Prompt: Write a Python function safe_mean_000034(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_000034([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=44 and h=1.45, 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 = 14.4 kg and a = 12.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 186.48, "unit": "N"}

Answer: 186.48

Prompt: A cart has mass 14.4 kg and measured acceleration 12.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 14.4 kg and a = 12.95 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 6.3^2 and multiply by 0.5 * 4.5.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 89.3025, "unit": "J"}

Answer: 89.3025

Prompt: A body of mass 4.5 kg moves at 6.3 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 6.3^2 and multiply by 0.5 * 4.5.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=71 degrees through the sine of 2 theta.
3. Substitute v=7.6 m/s and g=9.81 m/s^2.
Final: {"answer": 3.6249, "unit": "m"}

Answer: 3.6249

Prompt: A projectile is launched on level ground with no air resistance at speed 7.6 m/s and angle 71 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=71 degrees through the sine of 2 theta.
Substitute v=7.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.46 * 8.314 * 482 / 94.0.
Final: {"answer": 232.7672, "unit": "kPa"}

Answer: 232.7672

Prompt: An ideal gas sample has n=5.46 mol, T=482 K, and V=94.0 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 = 5.46 * 8.314 * 482 / 94.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 55 * 4.66 * 75.
Final: {"answer": 19222.5, "unit": "J"}

Answer: 19222.5

Prompt: A 55 g sample has specific heat 4.66 J/(g*K). How much heat is needed to raise its temperature by 75 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 55 * 4.66 * 75.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=562 mg, t=287 h, and T_half=68.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 30.7954, "unit": "mg"}

Answer: 30.7954

Prompt: A radioactive sample starts with 562 mg. Its half-life is 68.5 hours. How many mg remain after 287 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=562 mg, t=287 h, and T_half=68.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.31 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 321.7131, "unit": "g"}

Answer: 321.7131

Prompt: A sample contains 7.31 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.31 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 3185 mL to 3.185 L.
3. Compute M = 4.765 / 3.185.
Final: {"answer": 1.4961, "unit": "mol/L"}

Answer: 1.4961

Prompt: A solution contains 4.765 mol of solute in 3185 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3185 mL to 3.185 L.
Compute M = 4.765 / 3.185.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-9.1)=19.8 and f(-6.3)=14.2.
3. The interval width is 2.8.
Final: {"answer": 47.6, "unit": "area_units"}

Answer: 47.6

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2x+1.6 from x=-9.1 to x=-6.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.1)=19.8 and f(-6.3)=14.2.
The interval width is 2.8.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.3 and add it to the current value.
Final: {"answer": [1.35, 1.81, 1.4], "unit": "temperature_units"}

Answer: 1.35

Answer: 1.81

Answer: 1.4

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.2, right=1.9; current interior values are [2.85, 1.9, 0.65]. Use r=0.3. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 19254.0 / 1000.
Final: {"answer": 19.254, "unit": "kg"}

Answer: 19.254

Prompt: Convert 19254 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 19254.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=90 degrees and keep the unit as newtons.
Final: {"answer": [0.0, 289.5], "unit": "N"}

Answer: 0.0

Answer: 289.5

Prompt: A vector has magnitude 289.5 N at 90 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=90 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": [0.0, -20.75], "unit": "dimensionless"}

Answer: 0.0

Answer: -20.75

Prompt: A line passes through points (3.25, -20.75) and (16, -20.75). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In lab notebook case 476206, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def pairwise_ratios_000052(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_000052"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_000052(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_000052([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_000052([1, 2], [1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 registry survey records in release 430157, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 16.5 kg and a = 2.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 48.675, "unit": "N"}

Answer: 48.675

Prompt: A cart has mass 16.5 kg and measured acceleration 2.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 16.5 kg and a = 2.95 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 13.8^2 and multiply by 0.5 * 24.45.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2328.129, "unit": "J"}

Answer: 2328.129

Prompt: A body of mass 24.45 kg moves at 13.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 13.8^2 and multiply by 0.5 * 24.45.
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 = 1570 * 1.775 * 1.
Final: {"answer": 2786.75, "unit": "J"}

Answer: 2786.75

Prompt: A 1570 g sample has specific heat 1.775 J/(g*K). How much heat is needed to raise its temperature by 1 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1570 * 1.775 * 1.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=173.3 V and R=22.3 ohm.
Final: {"answer": 1346.7664, "unit": "W"}

Answer: 1346.7664

Prompt: A resistor has resistance 22.3 ohm and voltage 173.3 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=173.3 V and R=22.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=393 mg, t=221 h, and T_half=109.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 97.014, "unit": "mg"}

Answer: 97.014

Prompt: A radioactive sample starts with 393 mg. Its half-life is 109.5 hours. How many mg remain after 221 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=393 mg, t=221 h, and T_half=109.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.27 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 769.2661, "unit": "g"}

Answer: 769.2661

Prompt: A sample contains 4.27 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 = 4.27 mol * 180.156 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) = -0.86 y, so each step multiplies y by 1 - h*0.86.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 1.4324, "unit": "state_units"}

Answer: 1.4324

Prompt: Use explicit Euler on dy/dt = -0.86 y with y(0)=6, step size h=0.35, 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) = -0.86 y, so each step multiplies y by 1 - h*0.86.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-8.3)=-11.13 and f(0.3)=6.93.
3. The interval width is 8.6.
Final: {"answer": -18.06, "unit": "area_units"}

Answer: -18.06

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2.1x+6.3 from x=-8.3 to x=0.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-8.3)=-11.13 and f(0.3)=6.93.
The interval width is 8.6.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.34 and add it to the current value.
Final: {"answer": [0.809, 1.448, 0.869], "unit": "temperature_units"}

Answer: 0.809

Answer: 1.448

Answer: 0.869

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=-1.9, right=1.1; current interior values are [2.9, 1.55, -0.1]. 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. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4181.5 / 100.
Final: {"answer": 41.815, "unit": "m"}

Answer: 41.815

Prompt: Convert 4181.5 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 4181.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=233 degrees and keep the unit as newtons.
Final: {"answer": [-133.0011, -176.4984], "unit": "N"}

Answer: -133.0011

Answer: -176.4984

Prompt: A vector has magnitude 221 N at 233 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=233 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-4.0, -0.75], "unit": "dimensionless"}

Answer: -4.0

Answer: -0.75

Prompt: A line passes through points (18.25, -73.75) and (24.75, -99.75). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In quality-control check case 89868, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def normalize_000070(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_000070"}

Answer: python_code

Prompt: Write a Python function normalize_000070(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_000070([2, 3, 5]); assert len(out) == 3

try:
    normalize_000070([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.12 and interior values [-1.45, -0.9, -1.3], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 20.6 kg and a = 12.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 249.26, "unit": "N"}

Answer: 249.26

Prompt: A cart has mass 20.6 kg and measured acceleration 12.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 20.6 kg and a = 12.1 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 25.6^2 and multiply by 0.5 * 19.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 6225.92, "unit": "J"}

Answer: 6225.92

Prompt: A body of mass 19 kg moves at 25.6 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 25.6^2 and multiply by 0.5 * 19.
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=59 degrees through the sine of 2 theta.
3. Substitute v=11.3 m/s and g=9.81 m/s^2.
Final: {"answer": 11.4927, "unit": "m"}

Answer: 11.4927

Prompt: A projectile is launched on level ground with no air resistance at speed 11.3 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=11.3 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=987 mg, t=86.5 h, and T_half=80.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 468.6516, "unit": "mg"}

Answer: 468.6516

Prompt: A radioactive sample starts with 987 mg. Its half-life is 80.5 hours. How many mg remain after 86.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=987 mg, t=86.5 h, and T_half=80.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.29 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 629.5472, "unit": "g"}

Answer: 629.5472

Prompt: A sample contains 6.29 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.29 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1180 mL to 1.18 L.
3. Compute M = 2.735 / 1.18.
Final: {"answer": 2.3178, "unit": "mol/L"}

Answer: 2.3178

Prompt: A solution contains 2.735 mol of solute in 1180 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1180 mL to 1.18 L.
Compute M = 2.735 / 1.18.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 17.6153, "unit": "state_units"}

Answer: 17.6153

Prompt: Use explicit Euler on dy/dt = -0.17 y with y(0)=66.5, step size h=0.9, 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) = -0.17 y, so each step multiplies y by 1 - h*0.17.
Apply that update for 8 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-9.9)=33.73 and f(-2.5)=13.75.
3. The interval width is 7.4.
Final: {"answer": 175.676, "unit": "area_units"}

Answer: 175.676

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.7x+7 from x=-9.9 to x=-2.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.9)=33.73 and f(-2.5)=13.75.
The interval width is 7.4.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 44644.0 / 1000.
Final: {"answer": 44.644, "unit": "kg"}

Answer: 44.644

Prompt: Convert 44644 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 44644.0 / 1000.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-8.7, 20.25], "unit": "dimensionless"}

Answer: -8.7

Answer: 20.25

Prompt: A line passes through points (1.75, 5.025) and (7.5, -45). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. 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=1.71 mol and T=579 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 = 5.8 kg and a = 13.4 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 77.72, "unit": "N"}

Answer: 77.72

Prompt: A cart has mass 5.8 kg and measured acceleration 13.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 5.8 kg and a = 13.4 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 9.25^2 and multiply by 0.5 * 20.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 891.9891, "unit": "J"}

Answer: 891.9891

Prompt: A body of mass 20.85 kg moves at 9.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 9.25^2 and multiply by 0.5 * 20.85.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=75 degrees through the sine of 2 theta.
3. Substitute v=74.5 m/s and g=9.81 m/s^2.
Final: {"answer": 282.8874, "unit": "m"}

Answer: 282.8874

Prompt: A projectile is launched on level ground with no air resistance at speed 74.5 m/s and angle 75 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=75 degrees through the sine of 2 theta.
Substitute v=74.5 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.42 * 8.314 * 570 / 72.9.
Final: {"answer": 352.3357, "unit": "kPa"}

Answer: 352.3357

Prompt: An ideal gas sample has n=5.42 mol, T=570 K, and V=72.9 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 = 5.42 * 8.314 * 570 / 72.9.


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=91.1 V and R=111.4 ohm.
Final: {"answer": 74.4992, "unit": "W"}

Answer: 74.4992

Prompt: A resistor has resistance 111.4 ohm and voltage 91.1 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=91.1 V and R=111.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=754.5 mg, t=143 h, and T_half=84.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 233.4661, "unit": "mg"}

Answer: 233.4661

Prompt: A radioactive sample starts with 754.5 mg. Its half-life is 84.5 hours. How many mg remain after 143 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=754.5 mg, t=143 h, and T_half=84.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 355 mL to 0.355 L.
3. Compute M = 4.355 / 0.355.
Final: {"answer": 12.2676, "unit": "mol/L"}

Answer: 12.2676

Prompt: A solution contains 4.355 mol of solute in 355 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 355 mL to 0.355 L.
Compute M = 4.355 / 0.355.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.87 y, so each step multiplies y by 1 - h*0.87.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 3.8554, "unit": "state_units"}

Answer: 3.8554

Prompt: Use explicit Euler on dy/dt = -0.87 y with y(0)=47, step size h=0.65, for 3 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.87 y, so each step multiplies y by 1 - h*0.87.
Apply that update for 3 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(0.9)=-13.84 and f(6.1)=-6.56.
3. The interval width is 5.2.
Final: {"answer": -53.04, "unit": "area_units"}

Answer: -53.04

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.4x+-15.1 from x=0.9 to x=6.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(0.9)=-13.84 and f(6.1)=-6.56.
The interval width is 5.2.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.36 and add it to the current value.
Final: {"answer": [0.802, -0.128, -0.86], "unit": "temperature_units"}

Answer: 0.802

Answer: -0.128

Answer: -0.86

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=-0.2; current interior values are [1.9, -1.1, -1.4]. Use r=0.36. 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=0.36 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 114.5 + 273.15.
Final: {"answer": 387.65, "unit": "K"}

Answer: 387.65

Prompt: Convert 114.5 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 114.5 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=78 degrees and keep the unit as newtons.
Final: {"answer": [42.6219, 200.5203], "unit": "N"}

Answer: 42.6219

Answer: 200.5203

Prompt: A vector has magnitude 205 N at 78 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=78 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, -16.0], "unit": "dimensionless"}

Answer: -8.85

Answer: -16.0

Prompt: A line passes through points (-13.5, 103.475) and (-6.75, 43.7375). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In student derivation case 426072, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def clamp_000106(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_000106"}

Answer: python_code

Prompt: Write a Python function clamp_000106(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.

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

try:
    clamp_000106(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 warehouse crop record from batch 305743 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 14.45 kg and a = 5.15 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 74.4175, "unit": "N"}

Answer: 74.4175

Prompt: A cart has mass 14.45 kg and measured acceleration 5.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 14.45 kg and a = 5.15 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 6.7^2 and multiply by 0.5 * 15.45.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 346.7752, "unit": "J"}

Answer: 346.7752

Prompt: A body of mass 15.45 kg moves at 6.7 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 6.7^2 and multiply by 0.5 * 15.45.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.42 * 8.314 * 388 / 25.5.
Final: {"answer": 559.1442, "unit": "kPa"}

Answer: 559.1442

Prompt: An ideal gas sample has n=4.42 mol, T=388 K, and V=25.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.42 * 8.314 * 388 / 25.5.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=29.7 V and R=165.7 ohm.
Final: {"answer": 5.3234, "unit": "W"}

Answer: 5.3234

Prompt: A resistor has resistance 165.7 ohm and voltage 29.7 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=29.7 V and R=165.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=613.5 mg, t=233 h, and T_half=80.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 82.5107, "unit": "mg"}

Answer: 82.5107

Prompt: A radioactive sample starts with 613.5 mg. Its half-life is 80.5 hours. How many mg remain after 233 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=613.5 mg, t=233 h, and T_half=80.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.56 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 149.6064, "unit": "g"}

Answer: 149.6064

Prompt: A sample contains 2.56 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 2.56 mol * 58.44 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) = -0.88 y, so each step multiplies y by 1 - h*0.88.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.88 y with y(0)=11.5, 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) = -0.88 y, so each step multiplies y by 1 - h*0.88.
Apply that update for 12 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(3.3)=21.48 and f(12.8)=55.68.
3. The interval width is 9.5.
Final: {"answer": 366.51, "unit": "area_units"}

Answer: 366.51

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.6x+9.6 from x=3.3 to x=12.8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3.3)=21.48 and f(12.8)=55.68.
The interval width is 9.5.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.4 and add it to the current value.
Final: {"answer": [0.18, -0.7, -0.37], "unit": "temperature_units"}

Answer: 0.18

Answer: -0.7

Answer: -0.37

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=-1.9; current interior values are [-1.6, 1.4, -0.85]. Use r=0.4. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4606.5 / 100.
Final: {"answer": 46.065, "unit": "m"}

Answer: 46.065

Prompt: Convert 4606.5 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 4606.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=201 degrees and keep the unit as newtons.
Final: {"answer": [-397.7053, -152.6647], "unit": "N"}

Answer: -397.7053

Answer: -152.6647

Prompt: A vector has magnitude 426 N at 201 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=201 degrees and keep the unit as newtons.


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

Answer: inconsistent

Prompt: In instrument manual case 384919, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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=5.89 mol and T=458 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 = 23.65 kg and a = 12.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 297.99, "unit": "N"}

Answer: 297.99

Prompt: A cart has mass 23.65 kg and measured acceleration 12.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 23.65 kg and a = 12.6 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 3.15^2 and multiply by 0.5 * 8.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 43.9071, "unit": "J"}

Answer: 43.9071

Prompt: A body of mass 8.85 kg moves at 3.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 3.15^2 and multiply by 0.5 * 8.85.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=29 degrees through the sine of 2 theta.
3. Substitute v=78.1 m/s and g=9.81 m/s^2.
Final: {"answer": 527.2949, "unit": "m"}

Answer: 527.2949

Prompt: A projectile is launched on level ground with no air resistance at speed 78.1 m/s and angle 29 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=29 degrees through the sine of 2 theta.
Substitute v=78.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.8 * 8.314 * 371 / 28.6.
Final: {"answer": 194.129, "unit": "kPa"}

Answer: 194.129

Prompt: An ideal gas sample has n=1.8 mol, T=371 K, and V=28.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.8 * 8.314 * 371 / 28.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 525 * 3.36 * 108.
Final: {"answer": 190512.0, "unit": "J"}

Answer: 190512.0

Prompt: A 525 g sample has specific heat 3.36 J/(g*K). How much heat is needed to raise its temperature by 108 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 525 * 3.36 * 108.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.81 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 81.0705, "unit": "g"}

Answer: 81.0705

Prompt: A sample contains 0.81 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 = 0.81 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4545 mL to 4.545 L.
3. Compute M = 4.165 / 4.545.
Final: {"answer": 0.9164, "unit": "mol/L"}

Answer: 0.9164

Prompt: A solution contains 4.165 mol of solute in 4545 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4545 mL to 4.545 L.
Compute M = 4.165 / 4.545.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(2.5)=18.8 and f(11.6)=82.5.
3. The interval width is 9.1.
Final: {"answer": 460.915, "unit": "area_units"}

Answer: 460.915

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7x+1.3 from x=2.5 to x=11.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(2.5)=18.8 and f(11.6)=82.5.
The interval width is 9.1.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.22 and add it to the current value.
Final: {"answer": [-0.049, 0.97, 1.102], "unit": "temperature_units"}

Answer: -0.049

Answer: 0.97

Answer: 1.102

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2, right=-0.15; current interior values are [-1.6, 1.85, 1.3]. Use r=0.22. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 39476.0 / 1000.
Final: {"answer": 39.476, "unit": "kg"}

Answer: 39.476

Prompt: Convert 39476 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 39476.0 / 1000.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [9.3, 8.0], "unit": "dimensionless"}

Answer: 9.3

Answer: 8.0

Prompt: A line passes through points (-1.75, -8.275) and (8.75, 89.375). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In instrument manual case 746972, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
import math

def unit_vector_000142(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_000142"}

Answer: python_code

Prompt: Write a Python function unit_vector_000142(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_000142(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.12 and interior values [1.55, -0.5, 1.15], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 6.2 kg and a = 5.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 35.03, "unit": "N"}

Answer: 35.03

Prompt: A cart has mass 6.2 kg and measured acceleration 5.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 6.2 kg and a = 5.65 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 19.35^2 and multiply by 0.5 * 16.4.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3070.2645, "unit": "J"}

Answer: 3070.2645

Prompt: A body of mass 16.4 kg moves at 19.35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 19.35^2 and multiply by 0.5 * 16.4.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.73 * 8.314 * 395 / 41.6.
Final: {"answer": 373.4005, "unit": "kPa"}

Answer: 373.4005

Prompt: An ideal gas sample has n=4.73 mol, T=395 K, and V=41.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.73 * 8.314 * 395 / 41.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1135 * 4.61 * 49.
Final: {"answer": 256385.15, "unit": "J"}

Answer: 256385.15

Prompt: A 1135 g sample has specific heat 4.61 J/(g*K). How much heat is needed to raise its temperature by 49 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1135 * 4.61 * 49.


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=183 V and R=170.8 ohm.
Final: {"answer": 196.0714, "unit": "W"}

Answer: 196.0714

Prompt: A resistor has resistance 170.8 ohm and voltage 183 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=183 V and R=170.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=151.5 mg, t=317 h, and T_half=111 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 20.9274, "unit": "mg"}

Answer: 20.9274

Prompt: A radioactive sample starts with 151.5 mg. Its half-life is 111 hours. How many mg remain after 317 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=151.5 mg, t=317 h, and T_half=111 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.88 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 141.9582, "unit": "g"}

Answer: 141.9582

Prompt: A sample contains 7.88 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.88 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(-3.1)=22.27 and f(1.2)=-10.84.
3. The interval width is 4.3.
Final: {"answer": 24.5745, "unit": "area_units"}

Answer: 24.5745

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.7x+-1.6 from x=-3.1 to x=1.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-3.1)=22.27 and f(1.2)=-10.84.
The interval width is 4.3.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.42 and add it to the current value.
Final: {"answer": [1.07, 0.039, 0.379], "unit": "temperature_units"}

Answer: 1.07

Answer: 0.039

Answer: 0.379

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=-0.3, right=-1.85; current interior values are [-0.4, 3.0, -0.65]. Use r=0.42. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=309 degrees and keep the unit as newtons.
Final: {"answer": [229.3873, -283.2697], "unit": "N"}

Answer: 229.3873

Answer: -283.2697

Prompt: A vector has magnitude 364.5 N at 309 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=309 degrees and keep the unit as newtons.


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

Answer: inconsistent

Prompt: In quality-control check case 254165, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def safe_mean_000160(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_000160"}

Answer: python_code

Prompt: Write a Python function safe_mean_000160(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_000160([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=3.48 mol and T=407 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. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=76 degrees through the sine of 2 theta.
3. Substitute v=25 m/s and g=9.81 m/s^2.
Final: {"answer": 29.9103, "unit": "m"}

Answer: 29.9103

Prompt: A projectile is launched on level ground with no air resistance at speed 25 m/s and angle 76 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=76 degrees through the sine of 2 theta.
Substitute v=25 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 = 5.32 * 8.314 * 287 / 44.2.
Final: {"answer": 287.1979, "unit": "kPa"}

Answer: 287.1979

Prompt: An ideal gas sample has n=5.32 mol, T=287 K, and V=44.2 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 = 5.32 * 8.314 * 287 / 44.2.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=32.5 mg, t=86 h, and T_half=11 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.144, "unit": "mg"}

Answer: 0.144

Prompt: A radioactive sample starts with 32.5 mg. Its half-life is 11 hours. How many mg remain after 86 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=32.5 mg, t=86 h, and T_half=11 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.7 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 370.3219, "unit": "g"}

Answer: 370.3219

Prompt: A sample contains 3.7 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 = 3.7 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3600 mL to 3.6 L.
3. Compute M = 3.9 / 3.6.
Final: {"answer": 1.0833, "unit": "mol/L"}

Answer: 1.0833

Prompt: A solution contains 3.9 mol of solute in 3600 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3600 mL to 3.6 L.
Compute M = 3.9 / 3.6.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.23 y, so each step multiplies y by 1 - h*0.23.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 23.7239, "unit": "state_units"}

Answer: 23.7239

Prompt: Use explicit Euler on dy/dt = -0.23 y with y(0)=78, step size h=1.95, 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) = -0.23 y, so each step multiplies y by 1 - h*0.23.
Apply that update for 2 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(6.1)=31 and f(16)=110.2.
3. The interval width is 9.9.
Final: {"answer": 698.94, "unit": "area_units"}

Answer: 698.94

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=8x+-17.8 from x=6.1 to x=16. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.1)=31 and f(16)=110.2.
The interval width is 9.9.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.14 and add it to the current value.
Final: {"answer": [1.129, 1.716, 0.974], "unit": "temperature_units"}

Answer: 1.129

Answer: 1.716

Answer: 0.974

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=2.75; current interior values are [0.8, 2.15, 0.4]. Use r=0.14. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=1 degrees and keep the unit as newtons.
Final: {"answer": [74.4887, 1.3002], "unit": "N"}

Answer: 74.4887

Answer: 1.3002

Prompt: A vector has magnitude 74.5 N at 1 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=1 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-1.75, -8.5], "unit": "dimensionless"}

Answer: -1.75

Answer: -8.5

Prompt: A line passes through points (11.75, -29.0625) and (16.5, -37.375). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In model card equation case 227898, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def threshold_flags_000178(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_000178"}

Answer: python_code

Prompt: Write a Python function threshold_flags_000178(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.

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

assert threshold_flags_000178([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_000178([], 5) == []

assert threshold_flags_000178([-1, 0], 0) == [False, True]


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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=5.17 mol and T=415 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 = 2.6 kg and a = 5.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 13.78, "unit": "N"}

Answer: 13.78

Prompt: A cart has mass 2.6 kg and measured acceleration 5.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 2.6 kg and a = 5.3 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 4^2 and multiply by 0.5 * 21.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 173.6, "unit": "J"}

Answer: 173.6

Prompt: A body of mass 21.7 kg moves at 4 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 4^2 and multiply by 0.5 * 21.7.
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=26 degrees through the sine of 2 theta.
3. Substitute v=47.9 m/s and g=9.81 m/s^2.
Final: {"answer": 184.3037, "unit": "m"}

Answer: 184.3037

Prompt: A projectile is launched on level ground with no air resistance at speed 47.9 m/s and angle 26 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=26 degrees through the sine of 2 theta.
Substitute v=47.9 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.44 * 8.314 * 346 / 116.6.
Final: {"answer": 10.8553, "unit": "kPa"}

Answer: 10.8553

Prompt: An ideal gas sample has n=0.44 mol, T=346 K, and V=116.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.44 * 8.314 * 346 / 116.6.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=59.5 V and R=99.2 ohm.
Final: {"answer": 35.688, "unit": "W"}

Answer: 35.688

Prompt: A resistor has resistance 99.2 ohm and voltage 59.5 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=59.5 V and R=99.2 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=206 mg, t=170.5 h, and T_half=88 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 53.7801, "unit": "mg"}

Answer: 53.7801

Prompt: A radioactive sample starts with 206 mg. Its half-life is 88 hours. How many mg remain after 170.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=206 mg, t=170.5 h, and T_half=88 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.58 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 92.3352, "unit": "g"}

Answer: 92.3352

Prompt: A sample contains 1.58 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.58 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4710 mL to 4.71 L.
3. Compute M = 1.145 / 4.71.
Final: {"answer": 0.2431, "unit": "mol/L"}

Answer: 0.2431

Prompt: A solution contains 1.145 mol of solute in 4710 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4710 mL to 4.71 L.
Compute M = 1.145 / 4.71.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.59 y with y(0)=17, step size h=1.75, for 7 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.
Apply that update for 7 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6.4)=-10.9 and f(1.9)=-2.6.
3. The interval width is 8.3.
Final: {"answer": -56.025, "unit": "area_units"}

Answer: -56.025

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1x+-4.5 from x=-6.4 to x=1.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.4)=-10.9 and f(1.9)=-2.6.
The interval width is 8.3.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.06 and add it to the current value.
Final: {"answer": [0.296, -0.88, 1.4], "unit": "temperature_units"}

Answer: 0.296

Answer: -0.88

Answer: 1.4

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.25, right=-0.45; current interior values are [0.5, -1.15, 1.7]. Use r=0.06. Return the next interior vector.

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


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-0.4, -15.5], "unit": "dimensionless"}

Answer: -0.4

Answer: -15.5

Prompt: A line passes through points (12, -20.3) and (19, -23.1). 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. 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 82.7 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 = 10.9 kg and a = 7.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 81.205, "unit": "N"}

Answer: 81.205

Prompt: A cart has mass 10.9 kg and measured acceleration 7.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 10.9 kg and a = 7.45 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 11^2 and multiply by 0.5 * 21.55.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1303.775, "unit": "J"}

Answer: 1303.775

Prompt: A body of mass 21.55 kg moves at 11 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 11^2 and multiply by 0.5 * 21.55.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=43 degrees through the sine of 2 theta.
3. Substitute v=61.7 m/s and g=9.81 m/s^2.
Final: {"answer": 387.1169, "unit": "m"}

Answer: 387.1169

Prompt: A projectile is launched on level ground with no air resistance at speed 61.7 m/s and angle 43 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=43 degrees through the sine of 2 theta.
Substitute v=61.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.85 * 8.314 * 410 / 59.6.
Final: {"answer": 48.6146, "unit": "kPa"}

Answer: 48.6146

Prompt: An ideal gas sample has n=0.85 mol, T=410 K, and V=59.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.85 * 8.314 * 410 / 59.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 95 * 3.795 * 73.
Final: {"answer": 26318.325, "unit": "J"}

Answer: 26318.325

Prompt: A 95 g sample has specific heat 3.795 J/(g*K). How much heat is needed to raise its temperature by 73 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 95 * 3.795 * 73.


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=150.6 V and R=127.4 ohm.
Final: {"answer": 178.0248, "unit": "W"}

Answer: 178.0248

Prompt: A resistor has resistance 127.4 ohm and voltage 150.6 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=150.6 V and R=127.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=695.5 mg, t=301.5 h, and T_half=9.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0, "unit": "mg"}

Answer: 0.0

Prompt: A radioactive sample starts with 695.5 mg. Its half-life is 9.5 hours. How many mg remain after 301.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=695.5 mg, t=301.5 h, and T_half=9.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.87 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 33.6881, "unit": "g"}

Answer: 33.6881

Prompt: A sample contains 1.87 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 = 1.87 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 85 mL to 0.085 L.
3. Compute M = 3.38 / 0.085.
Final: {"answer": 39.7647, "unit": "mol/L"}

Answer: 39.7647

Prompt: A solution contains 3.38 mol of solute in 85 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 85 mL to 0.085 L.
Compute M = 3.38 / 0.085.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.39 y, so each step multiplies y by 1 - h*0.39.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 9.7577, "unit": "state_units"}

Answer: 9.7577

Prompt: Use explicit Euler on dy/dt = -0.39 y with y(0)=37, step size h=0.6, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.39 y, so each step multiplies y by 1 - h*0.39.
Apply that update for 5 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(6.7)=9.5 and f(14.4)=40.3.
3. The interval width is 7.7.
Final: {"answer": 191.73, "unit": "area_units"}

Answer: 191.73

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4x+-17.3 from x=6.7 to x=14.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.7)=9.5 and f(14.4)=40.3.
The interval width is 7.7.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 1180.0 / 1000.
Final: {"answer": 1.18, "unit": "kg"}

Answer: 1.18

Prompt: Convert 1180 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 1180.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=20 degrees and keep the unit as newtons.
Final: {"answer": [93.9693, 34.202], "unit": "N"}

Answer: 93.9693

Answer: 34.202

Prompt: A vector has magnitude 100 N at 20 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=20 degrees and keep the unit as newtons.


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

```python
def threshold_flags_000214(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_000214"}

Answer: python_code

Prompt: Write a Python function threshold_flags_000214(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.

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

assert threshold_flags_000214([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_000214([], 5) == []

assert threshold_flags_000214([-1, 0], 0) == [False, True]


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 15.35 kg and a = 4.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 65.2375, "unit": "N"}

Answer: 65.2375

Prompt: A cart has mass 15.35 kg and measured acceleration 4.25 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 = 15.35 kg and a = 4.25 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 = 28.5^2 and multiply by 0.5 * 26.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 10681.0875, "unit": "J"}

Answer: 10681.0875

Prompt: A body of mass 26.3 kg moves at 28.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 28.5^2 and multiply by 0.5 * 26.3.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=48 degrees through the sine of 2 theta.
3. Substitute v=9.6 m/s and g=9.81 m/s^2.
Final: {"answer": 9.343, "unit": "m"}

Answer: 9.343

Prompt: A projectile is launched on level ground with no air resistance at speed 9.6 m/s and angle 48 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=48 degrees through the sine of 2 theta.
Substitute v=9.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.06 * 8.314 * 431 / 58.2.
Final: {"answer": 249.9714, "unit": "kPa"}

Answer: 249.9714

Prompt: An ideal gas sample has n=4.06 mol, T=431 K, and V=58.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.06 * 8.314 * 431 / 58.2.


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=121.8 V and R=83.8 ohm.
Final: {"answer": 177.0315, "unit": "W"}

Answer: 177.0315

Prompt: A resistor has resistance 83.8 ohm and voltage 121.8 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=121.8 V and R=83.8 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.05 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 353.562, "unit": "g"}

Answer: 353.562

Prompt: A sample contains 6.05 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.05 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3645 mL to 3.645 L.
3. Compute M = 2.2 / 3.645.
Final: {"answer": 0.6036, "unit": "mol/L"}

Answer: 0.6036

Prompt: A solution contains 2.2 mol of solute in 3645 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3645 mL to 3.645 L.
Compute M = 2.2 / 3.645.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.01 y, so each step multiplies y by 1 - h*0.01.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 21.3597, "unit": "state_units"}

Answer: 21.3597

Prompt: Use explicit Euler on dy/dt = -0.01 y with y(0)=24.5, step size h=1.7, 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) = -0.01 y, so each step multiplies y by 1 - h*0.01.
Apply that update for 8 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-0.8)=21.24 and f(7.7)=-6.81.
3. The interval width is 8.5.
Final: {"answer": 61.3275, "unit": "area_units"}

Answer: 61.3275

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.3x+18.6 from x=-0.8 to x=7.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-0.8)=21.24 and f(7.7)=-6.81.
The interval width is 8.5.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.16 and add it to the current value.
Final: {"answer": [-1.044, -0.964, 1.612], "unit": "temperature_units"}

Answer: -1.044

Answer: -0.964

Answer: 1.612

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=2; current interior values are [-1.1, -1.7, 2.3]. Use r=0.16. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 6616.0 / 1000.
Final: {"answer": 6.616, "unit": "kg"}

Answer: 6.616

Prompt: Convert 6616 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 6616.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=199 degrees and keep the unit as newtons.
Final: {"answer": [-361.1881, -124.367], "unit": "N"}

Answer: -361.1881

Answer: -124.367

Prompt: A vector has magnitude 382 N at 199 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=199 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-3.7, 20.5], "unit": "dimensionless"}

Answer: -3.7

Answer: 20.5

Prompt: A line passes through points (-16.5, 81.55) and (-14.5, 74.15). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In instrument manual case 664878, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def finite_differences_000232(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_000232"}

Answer: python_code

Prompt: Write a Python function finite_differences_000232(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_000232([5]) == []

assert finite_differences_000232([]) == []


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=0.28 and interior values [1.55, 1.25, -1.15], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 6.45 kg and a = 11.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 71.595, "unit": "N"}

Answer: 71.595

Prompt: A cart has mass 6.45 kg and measured acceleration 11.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 6.45 kg and a = 11.1 m/s^2.
The unit kg*m/s^2 is one newton.