Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 18.8^2 and multiply by 0.5 * 11.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2085.296, "unit": "J"}

Answer: 2085.296

Prompt: A body of mass 11.8 kg moves at 18.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 18.8^2 and multiply by 0.5 * 11.8.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=15 degrees through the sine of 2 theta.
3. Substitute v=50.4 m/s and g=9.81 m/s^2.
Final: {"answer": 129.4679, "unit": "m"}

Answer: 129.4679

Prompt: A projectile is launched on level ground with no air resistance at speed 50.4 m/s and angle 15 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=15 degrees through the sine of 2 theta.
Substitute v=50.4 m/s and g=9.81 m/s^2.

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


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.33 * 8.314 * 269 / 84.9.
Final: {"answer": 8.693, "unit": "kPa"}

Answer: 8.693

Prompt: An ideal gas sample has n=0.33 mol, T=269 K, and V=84.9 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 = 0.33 * 8.314 * 269 / 84.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 170 * 3.165 * 25.
Final: {"answer": 13451.25, "unit": "J"}

Answer: 13451.25

Prompt: A 170 g sample has specific heat 3.165 J/(g*K). How much heat is needed to raise its temperature by 25 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 170 * 3.165 * 25.


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=84.2 V and R=167.8 ohm.
Final: {"answer": 42.2505, "unit": "W"}

Answer: 42.2505

Prompt: A resistor has resistance 167.8 ohm and voltage 84.2 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=84.2 V and R=167.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=447.5 mg, t=24.5 h, and T_half=108 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 382.3876, "unit": "mg"}

Answer: 382.3876

Prompt: A radioactive sample starts with 447.5 mg. Its half-life is 108 hours. How many mg remain after 24.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=447.5 mg, t=24.5 h, and T_half=108 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 = 3.63 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 212.1372, "unit": "g"}

Answer: 212.1372

Prompt: A sample contains 3.63 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 = 3.63 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 4640 mL to 4.64 L.
3. Compute M = 3.795 / 4.64.
Final: {"answer": 0.8179, "unit": "mol/L"}

Answer: 0.8179

Prompt: A solution contains 3.795 mol of solute in 4640 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4640 mL to 4.64 L.
Compute M = 3.795 / 4.64.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 0.0049, "unit": "state_units"}

Answer: 0.0049

Prompt: Use explicit Euler on dy/dt = -0.63 y with y(0)=29.5, step size h=1.5, 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) = -0.63 y, so each step multiplies y by 1 - h*0.63.
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(-9.5)=-20.15 and f(-4.4)=-6.38.
3. The interval width is 5.1.
Final: {"answer": -67.6515, "unit": "area_units"}

Answer: -67.6515

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2.7x+5.5 from x=-9.5 to x=-4.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.5)=-20.15 and f(-4.4)=-6.38.
The interval width is 5.1.

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


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.12 and add it to the current value.
Final: {"answer": [-0.968, 0.654, -0.98], "unit": "temperature_units"}

Answer: -0.968

Answer: 0.654

Answer: -0.98

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=-0.55, right=1.25; current interior values are [-1.4, 1.35, -1.7]. Use r=0.12. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 146.0 + 273.15.
Final: {"answer": 419.15, "unit": "K"}

Answer: 419.15

Prompt: Convert 146 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 146.0 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=45 degrees and keep the unit as newtons.
Final: {"answer": [106.7731, 106.7731], "unit": "N"}

Answer: 106.7731

Answer: 106.7731

Prompt: A vector has magnitude 151 N at 45 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=45 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": [-4.1, -21.75], "unit": "dimensionless"}

Answer: -4.1

Answer: -21.75

Prompt: A line passes through points (-7.75, 10.025) and (3.75, -37.125). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In sensor calibration case 970201, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def running_total_002680(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_002680"}

Answer: python_code

Prompt: Write a Python function running_total_002680(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

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


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

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a scheduler scoring problem with 2429 items and budget 54415, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 39.05^2 and multiply by 0.5 * 15.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 11665.5041, "unit": "J"}

Answer: 11665.5041

Prompt: A body of mass 15.3 kg moves at 39.05 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 39.05^2 and multiply by 0.5 * 15.3.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=29 degrees through the sine of 2 theta.
3. Substitute v=27.2 m/s and g=9.81 m/s^2.
Final: {"answer": 63.9572, "unit": "m"}

Answer: 63.9572

Prompt: A projectile is launched on level ground with no air resistance at speed 27.2 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=27.2 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=63.2 V and R=115.5 ohm.
Final: {"answer": 34.5822, "unit": "W"}

Answer: 34.5822

Prompt: A resistor has resistance 115.5 ohm and voltage 63.2 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=63.2 V and R=115.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=170 mg, t=321 h, and T_half=38 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.487, "unit": "mg"}

Answer: 0.487

Prompt: A radioactive sample starts with 170 mg. Its half-life is 38 hours. How many mg remain after 321 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=170 mg, t=321 h, and T_half=38 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 4815 mL to 4.815 L.
3. Compute M = 4.295 / 4.815.
Final: {"answer": 0.892, "unit": "mol/L"}

Answer: 0.892

Prompt: A solution contains 4.295 mol of solute in 4815 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4815 mL to 4.815 L.
Compute M = 4.295 / 4.815.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.99 y, so each step multiplies y by 1 - h*0.99.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 28.9164, "unit": "state_units"}

Answer: 28.9164

Prompt: Use explicit Euler on dy/dt = -0.99 y with y(0)=48, step size h=1.9, 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) = -0.99 y, so each step multiplies y by 1 - h*0.99.
Apply that update for 4 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=0.26 and add it to the current value.
Final: {"answer": [2.401, 1.259, -0.419], "unit": "temperature_units"}

Answer: 2.401

Answer: 1.259

Answer: -0.419

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=2.25, right=-0.75; current interior values are [2.7, 2.0, -1.55]. Use r=0.26. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 235.5 + 273.15.
Final: {"answer": 508.65, "unit": "K"}

Answer: 508.65

Prompt: Convert 235.5 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 235.5 + 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=188 degrees and keep the unit as newtons.
Final: {"answer": [-111.4052, -15.657], "unit": "N"}

Answer: -111.4052

Answer: -15.657

Prompt: A vector has magnitude 112.5 N at 188 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=188 degrees and keep the unit as newtons.


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

Answer: consistent

Prompt: In sensor calibration case 444283, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def pairwise_ratios_002698(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_002698"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_002698(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_002698([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_002698([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 mobile clinical records in release 286042, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 0.5 kg and a = 12.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 6.15, "unit": "N"}

Answer: 6.15

Prompt: A cart has mass 0.5 kg and measured acceleration 12.3 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 = 0.5 kg and a = 12.3 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 = 19.25^2 and multiply by 0.5 * 29.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5530.6453, "unit": "J"}

Answer: 5530.6453

Prompt: A body of mass 29.85 kg moves at 19.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 19.25^2 and multiply by 0.5 * 29.85.
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=68 degrees through the sine of 2 theta.
3. Substitute v=5.6 m/s and g=9.81 m/s^2.
Final: {"answer": 2.2206, "unit": "m"}

Answer: 2.2206

Prompt: A projectile is launched on level ground with no air resistance at speed 5.6 m/s and angle 68 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=68 degrees through the sine of 2 theta.
Substitute v=5.6 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=104.8 V and R=97.5 ohm.
Final: {"answer": 112.6466, "unit": "W"}

Answer: 112.6466

Prompt: A resistor has resistance 97.5 ohm and voltage 104.8 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=104.8 V and R=97.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=382.5 mg, t=226.5 h, and T_half=11.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0005, "unit": "mg"}

Answer: 0.0005

Prompt: A radioactive sample starts with 382.5 mg. Its half-life is 11.5 hours. How many mg remain after 226.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=382.5 mg, t=226.5 h, and T_half=11.5 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 = 2.35 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 235.2045, "unit": "g"}

Answer: 235.2045

Prompt: A sample contains 2.35 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 = 2.35 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 1690 mL to 1.69 L.
3. Compute M = 3.35 / 1.69.
Final: {"answer": 1.9822, "unit": "mol/L"}

Answer: 1.9822

Prompt: A solution contains 3.35 mol of solute in 1690 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1690 mL to 1.69 L.
Compute M = 3.35 / 1.69.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.2 y, so each step multiplies y by 1 - h*0.2.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 13.005, "unit": "state_units"}

Answer: 13.005

Prompt: Use explicit Euler on dy/dt = -0.2 y with y(0)=18, step size h=0.75, for 2 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.2 y, so each step multiplies y by 1 - h*0.2.
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(-1)=4.6 and f(6.7)=-16.19.
3. The interval width is 7.7.
Final: {"answer": -44.6215, "unit": "area_units"}

Answer: -44.6215

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.7x+1.9 from x=-1 to x=6.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-1)=4.6 and f(6.7)=-16.19.
The interval width is 7.7.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.34 and add it to the current value.
Final: {"answer": [0.525, -0.108, -0.953], "unit": "temperature_units"}

Answer: 0.525

Answer: -0.108

Answer: -0.953

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=0.45, right=0.15; current interior values are [2.65, -1.4, -1.65]. 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. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=196 degrees and keep the unit as newtons.
Final: {"answer": [-133.6154, -38.3136], "unit": "N"}

Answer: -133.6154

Answer: -38.3136

Prompt: A vector has magnitude 139 N at 196 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=196 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-7.75, 15.0], "unit": "dimensionless"}

Answer: -7.75

Answer: 15.0

Prompt: A line passes through points (9.75, -60.5625) and (17.25, -118.688). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In quality-control check case 21672, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=4.98 mol and T=394 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 = 11.75 kg and a = 2.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 27.025, "unit": "N"}

Answer: 27.025

Prompt: A cart has mass 11.75 kg and measured acceleration 2.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 11.75 kg and a = 2.3 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 = 13.75^2 and multiply by 0.5 * 5.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 543.5547, "unit": "J"}

Answer: 543.5547

Prompt: A body of mass 5.75 kg moves at 13.75 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 13.75^2 and multiply by 0.5 * 5.75.
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 = 5.02 * 8.314 * 470 / 3.6.
Final: {"answer": 5448.9032, "unit": "kPa"}

Answer: 5448.9032

Prompt: An ideal gas sample has n=5.02 mol, T=470 K, and V=3.6 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 = 5.02 * 8.314 * 470 / 3.6.


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=63.9 V and R=180.3 ohm.
Final: {"answer": 22.6468, "unit": "W"}

Answer: 22.6468

Prompt: A resistor has resistance 180.3 ohm and voltage 63.9 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=63.9 V and R=180.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=917 mg, t=17.5 h, and T_half=54 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 732.5096, "unit": "mg"}

Answer: 732.5096

Prompt: A radioactive sample starts with 917 mg. Its half-life is 54 hours. How many mg remain after 17.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=917 mg, t=17.5 h, and T_half=54 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 = 7.96 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 465.1824, "unit": "g"}

Answer: 465.1824

Prompt: A sample contains 7.96 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 = 7.96 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) = -0.63 y, so each step multiplies y by 1 - h*0.63.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.63 y with y(0)=19.5, step size h=1.5, for 6 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-9)=-85.6 and f(-4.7)=-51.2.
3. The interval width is 4.3.
Final: {"answer": -294.12, "unit": "area_units"}

Answer: -294.12

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=8x+-13.6 from x=-9 to x=-4.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9)=-85.6 and f(-4.7)=-51.2.
The interval width is 4.3.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 8071.0 / 1000.
Final: {"answer": 8.071, "unit": "kg"}

Answer: 8.071

Prompt: Convert 8071 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 8071.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=147 degrees and keep the unit as newtons.
Final: {"answer": [-0.4193, 0.2723], "unit": "N"}

Answer: -0.4193

Answer: 0.2723

Prompt: A vector has magnitude 0.5 N at 147 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=147 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [1.0, 6.5], "unit": "dimensionless"}

Answer: 1.0

Answer: 6.5

Prompt: A line passes through points (-6.25, 0.25) and (-3.5, 3). 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 667439, 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_002734(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_002734"}

Answer: python_code

Prompt: Write a Python function finite_differences_002734(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_002734([5]) == []

assert finite_differences_002734([]) == []


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

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=70.5 and h=1.2, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 4.9 kg and a = 6.4 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 31.36, "unit": "N"}

Answer: 31.36

Prompt: A cart has mass 4.9 kg and measured acceleration 6.4 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 = 4.9 kg and a = 6.4 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 = 32.8^2 and multiply by 0.5 * 21.4.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 11511.488, "unit": "J"}

Answer: 11511.488

Prompt: A body of mass 21.4 kg moves at 32.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 32.8^2 and multiply by 0.5 * 21.4.
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=16 degrees through the sine of 2 theta.
3. Substitute v=38 m/s and g=9.81 m/s^2.
Final: {"answer": 78.0024, "unit": "m"}

Answer: 78.0024

Prompt: A projectile is launched on level ground with no air resistance at speed 38 m/s and angle 16 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=16 degrees through the sine of 2 theta.
Substitute v=38 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 = 4.39 * 8.314 * 488 / 18.3.
Final: {"answer": 973.2923, "unit": "kPa"}

Answer: 973.2923

Prompt: An ideal gas sample has n=4.39 mol, T=488 K, and V=18.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.39 * 8.314 * 488 / 18.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1050 * 2.37 * 1.
Final: {"answer": 2488.5, "unit": "J"}

Answer: 2488.5

Prompt: A 1050 g sample has specific heat 2.37 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 = 1050 * 2.37 * 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=79.7 V and R=74.9 ohm.
Final: {"answer": 84.8076, "unit": "W"}

Answer: 84.8076

Prompt: A resistor has resistance 74.9 ohm and voltage 79.7 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=79.7 V and R=74.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=839 mg, t=99.5 h, and T_half=26.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 62.1555, "unit": "mg"}

Answer: 62.1555

Prompt: A radioactive sample starts with 839 mg. Its half-life is 26.5 hours. How many mg remain after 99.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=839 mg, t=99.5 h, and T_half=26.5 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 = 6.22 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 273.7422, "unit": "g"}

Answer: 273.7422

Prompt: A sample contains 6.22 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.22 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 1125 mL to 1.125 L.
3. Compute M = 2.545 / 1.125.
Final: {"answer": 2.2622, "unit": "mol/L"}

Answer: 2.2622

Prompt: A solution contains 2.545 mol of solute in 1125 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1125 mL to 1.125 L.
Compute M = 2.545 / 1.125.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-7.6)=44.74 and f(-1.4)=23.66.
3. The interval width is 6.2.
Final: {"answer": 212.04, "unit": "area_units"}

Answer: 212.04

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.4x+18.9 from x=-7.6 to x=-1.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.6)=44.74 and f(-1.4)=23.66.
The interval width is 6.2.


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=0.44 and add it to the current value.
Final: {"answer": [1.208, 0.06, 0.894], "unit": "temperature_units"}

Answer: 1.208

Answer: 0.06

Answer: 0.894

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=0.95, right=-0.35; current interior values are [-1.3, 2.15, 0.85]. Use r=0.44. 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=0.44 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 6667.0 / 1000.
Final: {"answer": 6.667, "unit": "kg"}

Answer: 6.667

Prompt: Convert 6667 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 6667.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=222 degrees and keep the unit as newtons.
Final: {"answer": [-357.4527, -321.8518], "unit": "N"}

Answer: -357.4527

Answer: -321.8518

Prompt: A vector has magnitude 481 N at 222 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=222 degrees and keep the unit as newtons.


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 846799, 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 running_total_002752(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_002752"}

Answer: python_code

Prompt: Write a Python function running_total_002752(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 10^2 and multiply by 0.5 * 29.45.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1472.5, "unit": "J"}

Answer: 1472.5

Prompt: A body of mass 29.45 kg moves at 10 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 10^2 and multiply by 0.5 * 29.45.
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=32 degrees through the sine of 2 theta.
3. Substitute v=60.9 m/s and g=9.81 m/s^2.
Final: {"answer": 339.8019, "unit": "m"}

Answer: 339.8019

Prompt: A projectile is launched on level ground with no air resistance at speed 60.9 m/s and angle 32 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=32 degrees through the sine of 2 theta.
Substitute v=60.9 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 205 * 1.86 * 90.
Final: {"answer": 34317.0, "unit": "J"}

Answer: 34317.0

Prompt: A 205 g sample has specific heat 1.86 J/(g*K). How much heat is needed to raise its temperature by 90 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 205 * 1.86 * 90.


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=212.9 V and R=120.6 ohm.
Final: {"answer": 375.8409, "unit": "W"}

Answer: 375.8409

Prompt: A resistor has resistance 120.6 ohm and voltage 212.9 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=212.9 V and R=120.6 ohm.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.0705, "unit": "state_units"}

Answer: 0.0705

Prompt: Use explicit Euler on dy/dt = -0.21 y with y(0)=5.5, step size h=1.45, 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) = -0.21 y, so each step multiplies y by 1 - h*0.21.
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(8.7)=-53.08 and f(13)=-84.9.
3. The interval width is 4.3.
Final: {"answer": -296.657, "unit": "area_units"}

Answer: -296.657

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.4x+11.3 from x=8.7 to x=13. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(8.7)=-53.08 and f(13)=-84.9.
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=0.14 and add it to the current value.
Final: {"answer": [-0.461, -0.801, -0.294], "unit": "temperature_units"}

Answer: -0.461

Answer: -0.801

Answer: -0.294

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.7, right=0.55; current interior values are [-1.0, -0.85, -0.35]. 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=254 degrees and keep the unit as newtons.
Final: {"answer": [-15.0222, -52.3888], "unit": "N"}

Answer: -15.0222

Answer: -52.3888

Prompt: A vector has magnitude 54.5 N at 254 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=254 degrees and keep the unit as newtons.


Response:
Reasoning:
1. 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 billing survey record from batch 476214 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 36.85^2 and multiply by 0.5 * 6.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 4616.9365, "unit": "J"}

Answer: 4616.9365

Prompt: A body of mass 6.8 kg moves at 36.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 36.85^2 and multiply by 0.5 * 6.8.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=13 degrees through the sine of 2 theta.
3. Substitute v=20 m/s and g=9.81 m/s^2.
Final: {"answer": 17.8745, "unit": "m"}

Answer: 17.8745

Prompt: A projectile is launched on level ground with no air resistance at speed 20 m/s and angle 13 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=13 degrees through the sine of 2 theta.
Substitute v=20 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 = 5.82 * 8.314 * 448 / 93.4.
Final: {"answer": 232.0941, "unit": "kPa"}

Answer: 232.0941

Prompt: An ideal gas sample has n=5.82 mol, T=448 K, and V=93.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.82 * 8.314 * 448 / 93.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1370 * 2.625 * 114.
Final: {"answer": 409972.5, "unit": "J"}

Answer: 409972.5

Prompt: A 1370 g sample has specific heat 2.625 J/(g*K). How much heat is needed to raise its temperature by 114 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1370 * 2.625 * 114.


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=83.7 V and R=123.9 ohm.
Final: {"answer": 56.5431, "unit": "W"}

Answer: 56.5431

Prompt: A resistor has resistance 123.9 ohm and voltage 83.7 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=83.7 V and R=123.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=887.5 mg, t=44.5 h, and T_half=14.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 105.7591, "unit": "mg"}

Answer: 105.7591

Prompt: A radioactive sample starts with 887.5 mg. Its half-life is 14.5 hours. How many mg remain after 44.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=887.5 mg, t=44.5 h, and T_half=14.5 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 = 7.11 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 312.9111, "unit": "g"}

Answer: 312.9111

Prompt: A sample contains 7.11 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 = 7.11 mol * 44.01 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) = -0.81 y, so each step multiplies y by 1 - h*0.81.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.81 y with y(0)=36.5, step size h=1.05, for 10 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.81 y, so each step multiplies y by 1 - h*0.81.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-7.6)=50.36 and f(1.7)=-11.02.
3. The interval width is 9.3.
Final: {"answer": 182.931, "unit": "area_units"}

Answer: 182.931

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.6x+0.2 from x=-7.6 to x=1.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.6)=50.36 and f(1.7)=-11.02.
The interval width is 9.3.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.38 and add it to the current value.
Final: {"answer": [0.907, 0.916, 0.097], "unit": "temperature_units"}

Answer: 0.907

Answer: 0.916

Answer: 0.097

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=2.75, right=-1.15; current interior values are [-0.1, -0.3, 2.7]. Use r=0.38. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 12774.0 / 1000.
Final: {"answer": 12.774, "unit": "kg"}

Answer: 12.774

Prompt: Convert 12774 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 12774.0 / 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": [-5.8, 19.75], "unit": "dimensionless"}

Answer: -5.8

Answer: 19.75

Prompt: A line passes through points (7.5, -23.75) and (16.25, -74.5). Return [slope, intercept] for y = slope*x + intercept.

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


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

```python
import math

def unit_vector_002788(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_002788"}

Answer: python_code

Prompt: Write a Python function unit_vector_002788(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_002788(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=0.38 and interior values [1.9, 2.3, 2.6], 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 = 22.6 kg and a = 6.4 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 144.64, "unit": "N"}

Answer: 144.64

Prompt: A cart has mass 22.6 kg and measured acceleration 6.4 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 = 22.6 kg and a = 6.4 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 17.1^2 and multiply by 0.5 * 12.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1864.1138, "unit": "J"}

Answer: 1864.1138

Prompt: A body of mass 12.75 kg moves at 17.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 17.1^2 and multiply by 0.5 * 12.75.
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 = 1640 * 4.925 * 93.
Final: {"answer": 751161.0, "unit": "J"}

Answer: 751161.0

Prompt: A 1640 g sample has specific heat 4.925 J/(g*K). How much heat is needed to raise its temperature by 93 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1640 * 4.925 * 93.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=28.5 mg, t=289 h, and T_half=105.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 4.268, "unit": "mg"}

Answer: 4.268

Prompt: A radioactive sample starts with 28.5 mg. Its half-life is 105.5 hours. How many mg remain after 289 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=28.5 mg, t=289 h, and T_half=105.5 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 3715 mL to 3.715 L.
3. Compute M = 4.185 / 3.715.
Final: {"answer": 1.1265, "unit": "mol/L"}

Answer: 1.1265

Prompt: A solution contains 4.185 mol of solute in 3715 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3715 mL to 3.715 L.
Compute M = 4.185 / 3.715.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(3)=-15.7 and f(8.3)=-47.5.
3. The interval width is 5.3.
Final: {"answer": -167.48, "unit": "area_units"}

Answer: -167.48

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6x+2.3 from x=3 to x=8.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3)=-15.7 and f(8.3)=-47.5.
The interval width is 5.3.


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=0.2 and add it to the current value.
Final: {"answer": [-1.38, -0.52, 0.0], "unit": "temperature_units"}

Answer: -1.38

Answer: -0.52

Answer: 0.0

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.8, right=-1.1; current interior values are [-1.9, -0.4, 0.5]. Use r=0.2. 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=0.2 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=324 degrees and keep the unit as newtons.
Final: {"answer": [244.3231, -177.5111], "unit": "N"}

Answer: 244.3231

Answer: -177.5111

Prompt: A vector has magnitude 302 N at 324 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=324 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-0.8, -20.5], "unit": "dimensionless"}

Answer: -0.8

Answer: -20.5

Prompt: A line passes through points (11.5, -29.7) and (16.25, -33.5). 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 student derivation case 778535, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def weighted_sum_002806(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_002806"}

Answer: python_code

Prompt: Write a Python function weighted_sum_002806(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_002806([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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)=4 and h=2, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 44.5^2 and multiply by 0.5 * 8.4.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 8317.05, "unit": "J"}

Answer: 8317.05

Prompt: A body of mass 8.4 kg moves at 44.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 44.5^2 and multiply by 0.5 * 8.4.
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=60 degrees through the sine of 2 theta.
3. Substitute v=67.2 m/s and g=9.81 m/s^2.
Final: {"answer": 398.6577, "unit": "m"}

Answer: 398.6577

Prompt: A projectile is launched on level ground with no air resistance at speed 67.2 m/s and angle 60 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=60 degrees through the sine of 2 theta.
Substitute v=67.2 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.15 * 8.314 * 413 / 75.0.
Final: {"answer": 98.4322, "unit": "kPa"}

Answer: 98.4322

Prompt: An ideal gas sample has n=2.15 mol, T=413 K, and V=75.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.15 * 8.314 * 413 / 75.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1345 * 3.705 * 46.
Final: {"answer": 229228.35, "unit": "J"}

Answer: 229228.35

Prompt: A 1345 g sample has specific heat 3.705 J/(g*K). How much heat is needed to raise its temperature by 46 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1345 * 3.705 * 46.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=800.5 mg, t=133.5 h, and T_half=19.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 6.9577, "unit": "mg"}

Answer: 6.9577

Prompt: A radioactive sample starts with 800.5 mg. Its half-life is 19.5 hours. How many mg remain after 133.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=800.5 mg, t=133.5 h, and T_half=19.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.55 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 155.1349, "unit": "g"}

Answer: 155.1349

Prompt: A sample contains 1.55 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.55 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 3435 mL to 3.435 L.
3. Compute M = 0.305 / 3.435.
Final: {"answer": 0.0888, "unit": "mol/L"}

Answer: 0.0888

Prompt: A solution contains 0.305 mol of solute in 3435 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3435 mL to 3.435 L.
Compute M = 0.305 / 3.435.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-0.5)=-11.3 and f(4.5)=-51.3.
3. The interval width is 5.
Final: {"answer": -156.5, "unit": "area_units"}

Answer: -156.5

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-8x+-15.3 from x=-0.5 to x=4.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-0.5)=-11.3 and f(4.5)=-51.3.
The interval width is 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=0.36 and add it to the current value.
Final: {"answer": [1.012, 0.402, 1.476], "unit": "temperature_units"}

Answer: 1.012

Answer: 0.402

Answer: 1.476

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.4, right=1.55; current interior values are [-1.4, 1.5, 1.35]. 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. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 33175.0 / 1000.
Final: {"answer": 33.175, "unit": "kg"}

Answer: 33.175

Prompt: Convert 33175 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 33175.0 / 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": [9.65, -18.75], "unit": "dimensionless"}

Answer: 9.65

Answer: -18.75

Prompt: A line passes through points (-19.25, -204.513) and (-8.5, -100.775). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. density times acceleration times height gives kg/(m*s^2), or pascal
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In quality-control check case 141156, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def safe_mean_002824(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_002824"}

Answer: python_code

Prompt: Write a Python function safe_mean_002824(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_002824([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 7.65 kg and a = 1.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 12.6225, "unit": "N"}

Answer: 12.6225

Prompt: A cart has mass 7.65 kg and measured acceleration 1.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 7.65 kg and a = 1.65 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 = 1.35^2 and multiply by 0.5 * 11.65.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 10.6161, "unit": "J"}

Answer: 10.6161

Prompt: A body of mass 11.65 kg moves at 1.35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 1.35^2 and multiply by 0.5 * 11.65.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=16 degrees through the sine of 2 theta.
3. Substitute v=44.3 m/s and g=9.81 m/s^2.
Final: {"answer": 106.0103, "unit": "m"}

Answer: 106.0103

Prompt: A projectile is launched on level ground with no air resistance at speed 44.3 m/s and angle 16 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=16 degrees through the sine of 2 theta.
Substitute v=44.3 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1 * 8.314 * 542 / 103.6.
Final: {"answer": 43.496, "unit": "kPa"}

Answer: 43.496

Prompt: An ideal gas sample has n=1 mol, T=542 K, and V=103.6 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 * 8.314 * 542 / 103.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 790 * 0.515 * 57.
Final: {"answer": 23190.45, "unit": "J"}

Answer: 23190.45

Prompt: A 790 g sample has specific heat 0.515 J/(g*K). How much heat is needed to raise its temperature by 57 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 790 * 0.515 * 57.


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=140.7 V and R=194.4 ohm.
Final: {"answer": 101.8338, "unit": "W"}

Answer: 101.8338

Prompt: A resistor has resistance 194.4 ohm and voltage 140.7 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=140.7 V and R=194.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=142.5 mg, t=313 h, and T_half=82.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 10.2737, "unit": "mg"}

Answer: 10.2737

Prompt: A radioactive sample starts with 142.5 mg. Its half-life is 82.5 hours. How many mg remain after 313 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=142.5 mg, t=313 h, and T_half=82.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 8 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1441.248, "unit": "g"}

Answer: 1441.248

Prompt: A sample contains 8 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 = 8 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2400 mL to 2.4 L.
3. Compute M = 1.88 / 2.4.
Final: {"answer": 0.7833, "unit": "mol/L"}

Answer: 0.7833

Prompt: A solution contains 1.88 mol of solute in 2400 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2400 mL to 2.4 L.
Compute M = 1.88 / 2.4.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.09 y, so each step multiplies y by 1 - h*0.09.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 5.9798, "unit": "state_units"}

Answer: 5.9798

Prompt: Use explicit Euler on dy/dt = -0.09 y with y(0)=28, step size h=1.95, for 8 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.09 y, so each step multiplies y by 1 - h*0.09.
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(9.8)=5 and f(12.9)=9.65.
3. The interval width is 3.1.
Final: {"answer": 22.7075, "unit": "area_units"}

Answer: 22.7075

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.5x+-9.7 from x=9.8 to x=12.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.8)=5 and f(12.9)=9.65.
The interval width is 3.1.


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=0.4 and add it to the current value.
Final: {"answer": [-0.05, 0.2, -1.16], "unit": "temperature_units"}

Answer: -0.05

Answer: 0.2

Answer: -1.16

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.7, right=-0.65; current interior values are [2.15, -1.9, -0.7]. 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 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 22346.0 / 1000.
Final: {"answer": 22.346, "unit": "kg"}

Answer: 22.346

Prompt: Convert 22346 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 22346.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=137 degrees and keep the unit as newtons.
Final: {"answer": [-273.5263, 255.0674], "unit": "N"}

Answer: -273.5263

Answer: 255.0674

Prompt: A vector has magnitude 374 N at 137 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=137 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-5.4, -11.0], "unit": "dimensionless"}

Answer: -5.4

Answer: -11.0

Prompt: A line passes through points (10.25, -66.35) and (15.25, -93.35). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In quality-control check case 707097, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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=3.2 mol and T=613 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 = 3.8 kg and a = 10.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 38.95, "unit": "N"}

Answer: 38.95

Prompt: A cart has mass 3.8 kg and measured acceleration 10.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 3.8 kg and a = 10.25 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 34.65^2 and multiply by 0.5 * 27.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 16388.4971, "unit": "J"}

Answer: 16388.4971

Prompt: A body of mass 27.3 kg moves at 34.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 34.65^2 and multiply by 0.5 * 27.3.
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=60 degrees through the sine of 2 theta.
3. Substitute v=30.5 m/s and g=9.81 m/s^2.
Final: {"answer": 82.1223, "unit": "m"}

Answer: 82.1223

Prompt: A projectile is launched on level ground with no air resistance at speed 30.5 m/s and angle 60 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=60 degrees through the sine of 2 theta.
Substitute v=30.5 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.87 * 8.314 * 530 / 22.7.
Final: {"answer": 945.3421, "unit": "kPa"}

Answer: 945.3421

Prompt: An ideal gas sample has n=4.87 mol, T=530 K, and V=22.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.87 * 8.314 * 530 / 22.7.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1645 * 2.305 * 60.
Final: {"answer": 227503.5, "unit": "J"}

Answer: 227503.5

Prompt: A 1645 g sample has specific heat 2.305 J/(g*K). How much heat is needed to raise its temperature by 60 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1645 * 2.305 * 60.


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=2.4 V and R=139.6 ohm.
Final: {"answer": 0.0413, "unit": "W"}

Answer: 0.0413

Prompt: A resistor has resistance 139.6 ohm and voltage 2.4 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=2.4 V and R=139.6 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=732.5 mg, t=106.5 h, and T_half=112 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 378.9312, "unit": "mg"}

Answer: 378.9312

Prompt: A radioactive sample starts with 732.5 mg. Its half-life is 112 hours. How many mg remain after 106.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=732.5 mg, t=106.5 h, and T_half=112 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 = 7.89 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 347.2389, "unit": "g"}

Answer: 347.2389

Prompt: A sample contains 7.89 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 = 7.89 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 4295 mL to 4.295 L.
3. Compute M = 1.015 / 4.295.
Final: {"answer": 0.2363, "unit": "mol/L"}

Answer: 0.2363

Prompt: A solution contains 1.015 mol of solute in 4295 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4295 mL to 4.295 L.
Compute M = 1.015 / 4.295.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.34 y, so each step multiplies y by 1 - h*0.34.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 0.029, "unit": "state_units"}

Answer: 0.029

Prompt: Use explicit Euler on dy/dt = -0.34 y with y(0)=34, step size h=1.6, for 9 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.34 y, so each step multiplies y by 1 - h*0.34.
Apply that update for 9 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=0.4 and add it to the current value.
Final: {"answer": [1.0, -0.35, 1.21], "unit": "temperature_units"}

Answer: 1.0

Answer: -0.35

Answer: 1.21

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.75, right=0.75; current interior values are [-1.6, 2.55, -0.55]. Use r=0.4. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=9 degrees and keep the unit as newtons.
Final: {"answer": [406.4338, 64.3728], "unit": "N"}

Answer: 406.4338

Answer: 64.3728

Prompt: A vector has magnitude 411.5 N at 9 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=9 degrees and keep the unit as newtons.


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

Answer: consistent

Prompt: In simulation spec case 664451, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def safe_mean_002860(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_002860"}

Answer: python_code

Prompt: Write a Python function safe_mean_002860(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_002860([])
    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 mobile sensor records in release 624648, 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 = 24.45 kg and a = 14.2 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 347.19, "unit": "N"}

Answer: 347.19

Prompt: A cart has mass 24.45 kg and measured acceleration 14.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 24.45 kg and a = 14.2 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=34 degrees through the sine of 2 theta.
3. Substitute v=37.7 m/s and g=9.81 m/s^2.
Final: {"answer": 134.332, "unit": "m"}

Answer: 134.332

Prompt: A projectile is launched on level ground with no air resistance at speed 37.7 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=37.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 30 * 4.81 * 11.
Final: {"answer": 1587.3, "unit": "J"}

Answer: 1587.3

Prompt: A 30 g sample has specific heat 4.81 J/(g*K). How much heat is needed to raise its temperature by 11 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 30 * 4.81 * 11.


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=14.4 V and R=126 ohm.
Final: {"answer": 1.6457, "unit": "W"}

Answer: 1.6457

Prompt: A resistor has resistance 126 ohm and voltage 14.4 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=14.4 V and R=126 ohm.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2055 mL to 2.055 L.
3. Compute M = 2.36 / 2.055.
Final: {"answer": 1.1484, "unit": "mol/L"}

Answer: 1.1484

Prompt: A solution contains 2.36 mol of solute in 2055 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2055 mL to 2.055 L.
Compute M = 2.36 / 2.055.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.56 y, so each step multiplies y by 1 - h*0.56.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 0.0088, "unit": "state_units"}

Answer: 0.0088

Prompt: Use explicit Euler on dy/dt = -0.56 y with y(0)=79.5, step size h=1.7, 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) = -0.56 y, so each step multiplies y by 1 - h*0.56.
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(9.5)=20.2 and f(17.5)=45.8.
3. The interval width is 8.
Final: {"answer": 264.0, "unit": "area_units"}

Answer: 264.0

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.2x+-10.2 from x=9.5 to x=17.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.5)=20.2 and f(17.5)=45.8.
The interval width is 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=0.14 and add it to the current value.
Final: {"answer": [0.543, 0.021, 0.518], "unit": "temperature_units"}

Answer: 0.543

Answer: 0.021

Answer: 0.518

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=-0.4, right=-1.35; current interior values are [0.9, -0.35, 1.05]. 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=10 degrees and keep the unit as newtons.
Final: {"answer": [44.8088, 7.901], "unit": "N"}

Answer: 44.8088

Answer: 7.901

Prompt: A vector has magnitude 45.5 N at 10 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=10 degrees and keep the unit as newtons.


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

Answer: inconsistent

Prompt: In student derivation case 780435, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def finite_differences_002878(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_002878"}

Answer: python_code

Prompt: Write a Python function finite_differences_002878(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_002878([5]) == []

assert finite_differences_002878([]) == []


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)=21.5 and h=0.85, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 11.5 kg and a = 4.9 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 56.35, "unit": "N"}

Answer: 56.35

Prompt: A cart has mass 11.5 kg and measured acceleration 4.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 11.5 kg and a = 4.9 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 = 14.35^2 and multiply by 0.5 * 6.1.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 628.0636, "unit": "J"}

Answer: 628.0636

Prompt: A body of mass 6.1 kg moves at 14.35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 14.35^2 and multiply by 0.5 * 6.1.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=66 degrees through the sine of 2 theta.
3. Substitute v=37.8 m/s and g=9.81 m/s^2.
Final: {"answer": 108.2401, "unit": "m"}

Answer: 108.2401

Prompt: A projectile is launched on level ground with no air resistance at speed 37.8 m/s and angle 66 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=66 degrees through the sine of 2 theta.
Substitute v=37.8 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.52 * 8.314 * 281 / 84.7.
Final: {"answer": 97.0902, "unit": "kPa"}

Answer: 97.0902

Prompt: An ideal gas sample has n=3.52 mol, T=281 K, and V=84.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.52 * 8.314 * 281 / 84.7.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=219.3 V and R=54 ohm.
Final: {"answer": 890.6017, "unit": "W"}

Answer: 890.6017

Prompt: A resistor has resistance 54 ohm and voltage 219.3 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=219.3 V and R=54 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=986.5 mg, t=198.5 h, and T_half=57.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 90.1341, "unit": "mg"}

Answer: 90.1341

Prompt: A radioactive sample starts with 986.5 mg. Its half-life is 57.5 hours. How many mg remain after 198.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=986.5 mg, t=198.5 h, and T_half=57.5 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 3600 mL to 3.6 L.
3. Compute M = 3.705 / 3.6.
Final: {"answer": 1.0292, "unit": "mol/L"}

Answer: 1.0292

Prompt: A solution contains 3.705 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 = 3.705 / 3.6.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(6.2)=38.92 and f(7.3)=46.18.
3. The interval width is 1.1.
Final: {"answer": 46.805, "unit": "area_units"}

Answer: 46.805

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.6x+-2 from x=6.2 to x=7.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.2)=38.92 and f(7.3)=46.18.
The interval width is 1.1.


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=0.3 and add it to the current value.
Final: {"answer": [1.045, 0.53, -0.49], "unit": "temperature_units"}

Answer: 1.045

Answer: 0.53

Answer: -0.49

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=1.1, right=-1.35; current interior values are [2.65, -1.15, 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. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=218 degrees and keep the unit as newtons.
Final: {"answer": [-1.576, -1.2313], "unit": "N"}

Answer: -1.576

Answer: -1.2313

Prompt: A vector has magnitude 2 N at 218 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=218 degrees and keep the unit as newtons.


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

Answer: inconsistent

Prompt: In field worksheet case 959047, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def finite_differences_002896(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_002896"}

Answer: python_code

Prompt: Write a Python function finite_differences_002896(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_002896([5]) == []

assert finite_differences_002896([]) == []