Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.28 y, so each step multiplies y by 1 - h*0.28.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.1569, "unit": "state_units"}

Answer: 0.1569

Prompt: Use explicit Euler on dy/dt = -0.28 y with y(0)=61.5, step size h=1.4, for 12 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.28 y, so each step multiplies y by 1 - h*0.28.
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(-1.6)=-4.12 and f(3.4)=4.38.
3. The interval width is 5.
Final: {"answer": 0.65, "unit": "area_units"}

Answer: 0.65

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.7x+-1.4 from x=-1.6 to x=3.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-1.6)=-4.12 and f(3.4)=4.38.
The interval width is 5.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 15944.0 / 1000.
Final: {"answer": 15.944, "unit": "kg"}

Answer: 15.944

Prompt: Convert 15944 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 15944.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=174 degrees and keep the unit as newtons.
Final: {"answer": [-475.3815, 49.9646], "unit": "N"}

Answer: -475.3815

Answer: 49.9646

Prompt: A vector has magnitude 478 N at 174 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=174 degrees and keep the unit as newtons.

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


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-6.25, 8.5], "unit": "dimensionless"}

Answer: -6.25

Answer: 8.5

Prompt: A line passes through points (-4.75, 38.1875) and (3.75, -14.9375). 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 student derivation case 675143, 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_007378(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_007378"}

Answer: python_code

Prompt: Write a Python function running_total_007378(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

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


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

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 17.3 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 13.2 kg and a = 0.8 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 10.56, "unit": "N"}

Answer: 10.56

Prompt: A cart has mass 13.2 kg and measured acceleration 0.8 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 = 13.2 kg and a = 0.8 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 = 15.85^2 and multiply by 0.5 * 11.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1381.7237, "unit": "J"}

Answer: 1381.7237

Prompt: A body of mass 11 kg moves at 15.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 15.85^2 and multiply by 0.5 * 11.
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=21.6 m/s and g=9.81 m/s^2.
Final: {"answer": 40.3329, "unit": "m"}

Answer: 40.3329

Prompt: A projectile is launched on level ground with no air resistance at speed 21.6 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=21.6 m/s and g=9.81 m/s^2.

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


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.68 * 8.314 * 416 / 107.0.
Final: {"answer": 183.598, "unit": "kPa"}

Answer: 183.598

Prompt: An ideal gas sample has n=5.68 mol, T=416 K, and V=107.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.68 * 8.314 * 416 / 107.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 825 * 3.93 * 82.
Final: {"answer": 265864.5, "unit": "J"}

Answer: 265864.5

Prompt: A 825 g sample has specific heat 3.93 J/(g*K). How much heat is needed to raise its temperature by 82 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 825 * 3.93 * 82.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=122.4 V and R=138.3 ohm.
Final: {"answer": 108.328, "unit": "W"}

Answer: 108.328

Prompt: A resistor has resistance 138.3 ohm and voltage 122.4 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=122.4 V and R=138.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=613 mg, t=56 h, and T_half=39.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 229.4477, "unit": "mg"}

Answer: 229.4477

Prompt: A radioactive sample starts with 613 mg. Its half-life is 39.5 hours. How many mg remain after 56 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=613 mg, t=56 h, and T_half=39.5 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.06 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 3.5064, "unit": "g"}

Answer: 3.5064

Prompt: A sample contains 0.06 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 = 0.06 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(1.7)=11.23 and f(3.4)=14.46.
3. The interval width is 1.7.
Final: {"answer": 21.8365, "unit": "area_units"}

Answer: 21.8365

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.9x+8 from x=1.7 to x=3.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.7)=11.23 and f(3.4)=14.46.
The interval width is 1.7.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.12 and add it to the current value.
Final: {"answer": [1.208, 0.888, -0.398], "unit": "temperature_units"}

Answer: 1.208

Answer: 0.888

Answer: -0.398

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.15, right=-0.25; current interior values are [1.4, 1.05, -0.65]. Use r=0.12. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 780.5 / 100.
Final: {"answer": 7.805, "unit": "m"}

Answer: 7.805

Prompt: Convert 780.5 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 780.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=166 degrees and keep the unit as newtons.
Final: {"answer": [-448.2766, 111.7679], "unit": "N"}

Answer: -448.2766

Answer: 111.7679

Prompt: A vector has magnitude 462 N at 166 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=166 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 field worksheet case 112415, 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. 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 laboratory clinical record from batch 404925 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 22 kg and a = 0.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 18.7, "unit": "N"}

Answer: 18.7

Prompt: A cart has mass 22 kg and measured acceleration 0.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 22 kg and a = 0.85 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 39.8^2 and multiply by 0.5 * 5.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 4078.903, "unit": "J"}

Answer: 4078.903

Prompt: A body of mass 5.15 kg moves at 39.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 39.8^2 and multiply by 0.5 * 5.15.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=49 degrees through the sine of 2 theta.
3. Substitute v=29.3 m/s and g=9.81 m/s^2.
Final: {"answer": 86.6601, "unit": "m"}

Answer: 86.6601

Prompt: A projectile is launched on level ground with no air resistance at speed 29.3 m/s and angle 49 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=49 degrees through the sine of 2 theta.
Substitute v=29.3 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=48.9 V and R=66 ohm.
Final: {"answer": 36.2305, "unit": "W"}

Answer: 36.2305

Prompt: A resistor has resistance 66 ohm and voltage 48.9 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=48.9 V and R=66 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=558.5 mg, t=301.5 h, and T_half=69.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 27.6132, "unit": "mg"}

Answer: 27.6132

Prompt: A radioactive sample starts with 558.5 mg. Its half-life is 69.5 hours. How many mg remain after 301.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=558.5 mg, t=301.5 h, and T_half=69.5 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 = 5.08 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 915.1925, "unit": "g"}

Answer: 915.1925

Prompt: A sample contains 5.08 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.08 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 2940 mL to 2.94 L.
3. Compute M = 4.13 / 2.94.
Final: {"answer": 1.4048, "unit": "mol/L"}

Answer: 1.4048

Prompt: A solution contains 4.13 mol of solute in 2940 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2940 mL to 2.94 L.
Compute M = 4.13 / 2.94.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 0.0772, "unit": "state_units"}

Answer: 0.0772

Prompt: Use explicit Euler on dy/dt = -0.42 y with y(0)=11, step size h=1.1, 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) = -0.42 y, so each step multiplies y by 1 - h*0.42.
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(7.8)=42.3 and f(10.4)=61.8.
3. The interval width is 2.6.
Final: {"answer": 135.33, "unit": "area_units"}

Answer: 135.33

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.5x+-16.2 from x=7.8 to x=10.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7.8)=42.3 and f(10.4)=61.8.
The interval width is 2.6.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.32 and add it to the current value.
Final: {"answer": [-0.286, -0.196, -0.672], "unit": "temperature_units"}

Answer: -0.286

Answer: -0.196

Answer: -0.672

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.1, right=-1.25; current interior values are [0.45, -1.3, 0.4]. Use r=0.32. 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=0.32 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 551.5 / 100.
Final: {"answer": 5.515, "unit": "m"}

Answer: 5.515

Prompt: Convert 551.5 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 551.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=102 degrees and keep the unit as newtons.
Final: {"answer": [-96.0552, 451.9042], "unit": "N"}

Answer: -96.0552

Answer: 451.9042

Prompt: A vector has magnitude 462 N at 102 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=102 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": [2.35, -5.25], "unit": "dimensionless"}

Answer: 2.35

Answer: -5.25

Prompt: A line passes through points (-20, -52.25) and (-11.5, -32.275). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In sensor calibration case 563403, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 38.6 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 0.55 kg and a = 1.8 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 0.99, "unit": "N"}

Answer: 0.99

Prompt: A cart has mass 0.55 kg and measured acceleration 1.8 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 = 0.55 kg and a = 1.8 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 = 10.7^2 and multiply by 0.5 * 7.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 420.7507, "unit": "J"}

Answer: 420.7507

Prompt: A body of mass 7.35 kg moves at 10.7 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 10.7^2 and multiply by 0.5 * 7.35.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=75 degrees through the sine of 2 theta.
3. Substitute v=31.3 m/s and g=9.81 m/s^2.
Final: {"answer": 49.9332, "unit": "m"}

Answer: 49.9332

Prompt: A projectile is launched on level ground with no air resistance at speed 31.3 m/s and angle 75 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=75 degrees through the sine of 2 theta.
Substitute v=31.3 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 = 560 * 0.515 * 95.
Final: {"answer": 27398.0, "unit": "J"}

Answer: 27398.0

Prompt: A 560 g sample has specific heat 0.515 J/(g*K). How much heat is needed to raise its temperature by 95 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 560 * 0.515 * 95.


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=109.3 V and R=178.6 ohm.
Final: {"answer": 66.8896, "unit": "W"}

Answer: 66.8896

Prompt: A resistor has resistance 178.6 ohm and voltage 109.3 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=109.3 V and R=178.6 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 400.348, "unit": "g"}

Answer: 400.348

Prompt: A sample contains 4 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 = 4 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.68 y, so each step multiplies y by 1 - h*0.68.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": -0.0096, "unit": "state_units"}

Answer: -0.0096

Prompt: Use explicit Euler on dy/dt = -0.68 y with y(0)=53, step size h=1.9, for 7 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.68 y, so each step multiplies y by 1 - h*0.68.
Apply that update for 7 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-3.2)=3.92 and f(6)=-38.4.
3. The interval width is 9.2.
Final: {"answer": -158.608, "unit": "area_units"}

Answer: -158.608

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.6x+-10.8 from x=-3.2 to x=6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-3.2)=3.92 and f(6)=-38.4.
The interval width is 9.2.


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=0.42 and add it to the current value.
Final: {"answer": [-0.389, -0.684, -0.17], "unit": "temperature_units"}

Answer: -0.389

Answer: -0.684

Answer: -0.17

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=1.95; current interior values are [0.85, -1.65, -1.85]. Use r=0.42. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 55.0 + 273.15.
Final: {"answer": 328.15, "unit": "K"}

Answer: 328.15

Prompt: Convert 55 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 55.0 + 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=64 degrees and keep the unit as newtons.
Final: {"answer": [117.9218, 241.7756], "unit": "N"}

Answer: 117.9218

Answer: 241.7756

Prompt: A vector has magnitude 269 N at 64 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=64 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": [-10.0, -17.0], "unit": "dimensionless"}

Answer: -10.0

Answer: -17.0

Prompt: A line passes through points (1.5, -32) and (4.25, -59.5). 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. speed squared over acceleration has units of meters
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In instrument manual case 538333, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def weighted_sum_007432(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_007432"}

Answer: python_code

Prompt: Write a Python function weighted_sum_007432(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_007432([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: 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=4.62 mol and T=607 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 = 3.75 kg and a = 8.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 33.5625, "unit": "N"}

Answer: 33.5625

Prompt: A cart has mass 3.75 kg and measured acceleration 8.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 3.75 kg and a = 8.95 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=11 degrees through the sine of 2 theta.
3. Substitute v=39 m/s and g=9.81 m/s^2.
Final: {"answer": 58.0812, "unit": "m"}

Answer: 58.0812

Prompt: A projectile is launched on level ground with no air resistance at speed 39 m/s and angle 11 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=11 degrees through the sine of 2 theta.
Substitute v=39 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 = 3.4 * 8.314 * 584 / 79.9.
Final: {"answer": 206.6117, "unit": "kPa"}

Answer: 206.6117

Prompt: An ideal gas sample has n=3.4 mol, T=584 K, and V=79.9 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 = 3.4 * 8.314 * 584 / 79.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 165 * 1.82 * 43.
Final: {"answer": 12912.9, "unit": "J"}

Answer: 12912.9

Prompt: A 165 g sample has specific heat 1.82 J/(g*K). How much heat is needed to raise its temperature by 43 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 165 * 1.82 * 43.


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=171.3 V and R=71.8 ohm.
Final: {"answer": 408.6865, "unit": "W"}

Answer: 408.6865

Prompt: A resistor has resistance 71.8 ohm and voltage 171.3 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=171.3 V and R=71.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=467.5 mg, t=294 h, and T_half=46 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 5.5694, "unit": "mg"}

Answer: 5.5694

Prompt: A radioactive sample starts with 467.5 mg. Its half-life is 46 hours. How many mg remain after 294 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=467.5 mg, t=294 h, and T_half=46 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.74 y, so each step multiplies y by 1 - h*0.74.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 1.2116, "unit": "state_units"}

Answer: 1.2116

Prompt: Use explicit Euler on dy/dt = -0.74 y with y(0)=77.5, step size h=0.5, 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) = -0.74 y, so each step multiplies y by 1 - h*0.74.
Apply that update for 9 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(0.5)=6.9 and f(5.6)=-0.24.
3. The interval width is 5.1.
Final: {"answer": 16.983, "unit": "area_units"}

Answer: 16.983

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.4x+7.6 from x=0.5 to x=5.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(0.5)=6.9 and f(5.6)=-0.24.
The interval width is 5.1.


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=0.38 and add it to the current value.
Final: {"answer": [0.515, 0.712, 1.105], "unit": "temperature_units"}

Answer: 0.515

Answer: 0.712

Answer: 1.105

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=1.05, right=2.35; current interior values are [0.8, -0.2, 1.2]. 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 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4159.0 / 100.
Final: {"answer": 41.59, "unit": "m"}

Answer: 41.59

Prompt: Convert 4159 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 4159.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=352 degrees and keep the unit as newtons.
Final: {"answer": [162.404, -22.8244], "unit": "N"}

Answer: 162.404

Answer: -22.8244

Prompt: A vector has magnitude 164 N at 352 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=352 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 466970, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def finite_differences_007450(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_007450"}

Answer: python_code

Prompt: Write a Python function finite_differences_007450(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_007450([5]) == []

assert finite_differences_007450([]) == []


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=5.5 mol and T=397 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. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 32.3^2 and multiply by 0.5 * 20.55.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 10719.8047, "unit": "J"}

Answer: 10719.8047

Prompt: A body of mass 20.55 kg moves at 32.3 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 32.3^2 and multiply by 0.5 * 20.55.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=49 degrees through the sine of 2 theta.
3. Substitute v=40.6 m/s and g=9.81 m/s^2.
Final: {"answer": 166.3933, "unit": "m"}

Answer: 166.3933

Prompt: A projectile is launched on level ground with no air resistance at speed 40.6 m/s and angle 49 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=49 degrees through the sine of 2 theta.
Substitute v=40.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.05 * 8.314 * 488 / 9.9.
Final: {"answer": 430.3125, "unit": "kPa"}

Answer: 430.3125

Prompt: An ideal gas sample has n=1.05 mol, T=488 K, and V=9.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.05 * 8.314 * 488 / 9.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1685 * 4.685 * 88.
Final: {"answer": 694691.8, "unit": "J"}

Answer: 694691.8

Prompt: A 1685 g sample has specific heat 4.685 J/(g*K). How much heat is needed to raise its temperature by 88 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1685 * 4.685 * 88.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=691 mg, t=283 h, and T_half=46.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 10.1719, "unit": "mg"}

Answer: 10.1719

Prompt: A radioactive sample starts with 691 mg. Its half-life is 46.5 hours. How many mg remain after 283 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=691 mg, t=283 h, and T_half=46.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.22 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 9.6822, "unit": "g"}

Answer: 9.6822

Prompt: A sample contains 0.22 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 = 0.22 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 4105 mL to 4.105 L.
3. Compute M = 0.49 / 4.105.
Final: {"answer": 0.1194, "unit": "mol/L"}

Answer: 0.1194

Prompt: A solution contains 0.49 mol of solute in 4105 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4105 mL to 4.105 L.
Compute M = 0.49 / 4.105.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -1 y, so each step multiplies y by 1 - h*1.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 45.5, "unit": "state_units"}

Answer: 45.5

Prompt: Use explicit Euler on dy/dt = -1 y with y(0)=45.5, step size h=2, 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) = -1 y, so each step multiplies y by 1 - h*1.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(6.6)=13.16 and f(8.1)=19.31.
3. The interval width is 1.5.
Final: {"answer": 24.3525, "unit": "area_units"}

Answer: 24.3525

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.1x+-13.9 from x=6.6 to x=8.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.6)=13.16 and f(8.1)=19.31.
The interval width is 1.5.


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=0.18 and add it to the current value.
Final: {"answer": [0.602, -0.508, -0.753], "unit": "temperature_units"}

Answer: 0.602

Answer: -0.508

Answer: -0.753

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.85, right=2; current interior values are [1.7, -0.85, -1.5]. Use r=0.18. Return the next interior vector.

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


Response:
Reasoning:
1. 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 733095, 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 pairwise_ratios_007468(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_007468"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_007468(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_007468([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_007468([1, 2], [1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.48 and interior values [2.0, 0.5, -1.4], 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. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 26.9^2 and multiply by 0.5 * 24.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 8936.5835, "unit": "J"}

Answer: 8936.5835

Prompt: A body of mass 24.7 kg moves at 26.9 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 26.9^2 and multiply by 0.5 * 24.7.
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 = 2.45 * 8.314 * 611 / 52.2.
Final: {"answer": 238.4223, "unit": "kPa"}

Answer: 238.4223

Prompt: An ideal gas sample has n=2.45 mol, T=611 K, and V=52.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.45 * 8.314 * 611 / 52.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1255 * 4.52 * 115.
Final: {"answer": 652349.0, "unit": "J"}

Answer: 652349.0

Prompt: A 1255 g sample has specific heat 4.52 J/(g*K). How much heat is needed to raise its temperature by 115 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1255 * 4.52 * 115.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=218.6 V and R=8.3 ohm.
Final: {"answer": 5757.3446, "unit": "W"}

Answer: 5757.3446

Prompt: A resistor has resistance 8.3 ohm and voltage 218.6 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=218.6 V and R=8.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=179.5 mg, t=21.5 h, and T_half=116 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 157.8593, "unit": "mg"}

Answer: 157.8593

Prompt: A radioactive sample starts with 179.5 mg. Its half-life is 116 hours. How many mg remain after 21.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=179.5 mg, t=21.5 h, and T_half=116 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 = 1.79 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 179.1557, "unit": "g"}

Answer: 179.1557

Prompt: A sample contains 1.79 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 = 1.79 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 2995 mL to 2.995 L.
3. Compute M = 2.66 / 2.995.
Final: {"answer": 0.8881, "unit": "mol/L"}

Answer: 0.8881

Prompt: A solution contains 2.66 mol of solute in 2995 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2995 mL to 2.995 L.
Compute M = 2.66 / 2.995.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.28 y, so each step multiplies y by 1 - h*0.28.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 0.1003, "unit": "state_units"}

Answer: 0.1003

Prompt: Use explicit Euler on dy/dt = -0.28 y with y(0)=1, step size h=1, for 7 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.28 y, so each step multiplies y by 1 - h*0.28.
Apply that update for 7 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(0.7)=-20.64 and f(10.2)=-60.54.
3. The interval width is 9.5.
Final: {"answer": -385.605, "unit": "area_units"}

Answer: -385.605

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.2x+-17.7 from x=0.7 to x=10.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(0.7)=-20.64 and f(10.2)=-60.54.
The interval width is 9.5.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.18 and add it to the current value.
Final: {"answer": [1.662, 0.87, 1.45], "unit": "temperature_units"}

Answer: 1.662

Answer: 0.87

Answer: 1.45

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=2.15, right=-0.45; current interior values are [1.95, 0.15, 2.35]. Use r=0.18. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 14172.0 / 1000.
Final: {"answer": 14.172, "unit": "kg"}

Answer: 14.172

Prompt: Convert 14172 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 14172.0 / 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": [-6.45, 10.5], "unit": "dimensionless"}

Answer: -6.45

Answer: 10.5

Prompt: A line passes through points (10.75, -58.8375) and (13.5, -76.575). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In instrument manual case 432359, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def threshold_flags_007486(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_007486"}

Answer: python_code

Prompt: Write a Python function threshold_flags_007486(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.

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

assert threshold_flags_007486([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_007486([], 5) == []

assert threshold_flags_007486([-1, 0], 0) == [False, True]


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

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a alignment scoring problem with 1588 items and budget 74040, 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 = 14.15^2 and multiply by 0.5 * 18.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1872.0804, "unit": "J"}

Answer: 1872.0804

Prompt: A body of mass 18.7 kg moves at 14.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 14.15^2 and multiply by 0.5 * 18.7.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=8 degrees through the sine of 2 theta.
3. Substitute v=7.9 m/s and g=9.81 m/s^2.
Final: {"answer": 1.7536, "unit": "m"}

Answer: 1.7536

Prompt: A projectile is launched on level ground with no air resistance at speed 7.9 m/s and angle 8 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=8 degrees through the sine of 2 theta.
Substitute v=7.9 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.96 * 8.314 * 485 / 35.0.
Final: {"answer": 686.6414, "unit": "kPa"}

Answer: 686.6414

Prompt: An ideal gas sample has n=5.96 mol, T=485 K, and V=35.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.96 * 8.314 * 485 / 35.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 220 * 4.32 * 5.
Final: {"answer": 4752.0, "unit": "J"}

Answer: 4752.0

Prompt: A 220 g sample has specific heat 4.32 J/(g*K). How much heat is needed to raise its temperature by 5 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 220 * 4.32 * 5.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=65.8 V and R=117 ohm.
Final: {"answer": 37.0055, "unit": "W"}

Answer: 37.0055

Prompt: A resistor has resistance 117 ohm and voltage 65.8 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=65.8 V and R=117 ohm.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 400 mL to 0.4 L.
3. Compute M = 2.745 / 0.4.
Final: {"answer": 6.8625, "unit": "mol/L"}

Answer: 6.8625

Prompt: A solution contains 2.745 mol of solute in 400 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 400 mL to 0.4 L.
Compute M = 2.745 / 0.4.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.74 y, so each step multiplies y by 1 - h*0.74.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 25.0295, "unit": "state_units"}

Answer: 25.0295

Prompt: Use explicit Euler on dy/dt = -0.74 y with y(0)=47.5, step size h=0.2, 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) = -0.74 y, so each step multiplies y by 1 - h*0.74.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(2.7)=40.25 and f(8.2)=81.5.
3. The interval width is 5.5.
Final: {"answer": 334.8125, "unit": "area_units"}

Answer: 334.8125

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.5x+20 from x=2.7 to x=8.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(2.7)=40.25 and f(8.2)=81.5.
The interval width is 5.5.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 8865.0 / 1000.
Final: {"answer": 8.865, "unit": "kg"}

Answer: 8.865

Prompt: Convert 8865 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 8865.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=65 degrees and keep the unit as newtons.
Final: {"answer": [201.5889, 432.3088], "unit": "N"}

Answer: 201.5889

Answer: 432.3088

Prompt: A vector has magnitude 477 N at 65 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=65 degrees and keep the unit as newtons.


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

Answer: consistent

Prompt: In lab notebook case 945398, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def safe_mean_007504(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_007504"}

Answer: python_code

Prompt: Write a Python function safe_mean_007504(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_007504([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 3.35 kg and a = 14.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 47.7375, "unit": "N"}

Answer: 47.7375

Prompt: A cart has mass 3.35 kg and measured acceleration 14.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 3.35 kg and a = 14.25 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 13.45^2 and multiply by 0.5 * 23.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2098.469, "unit": "J"}

Answer: 2098.469

Prompt: A body of mass 23.2 kg moves at 13.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 13.45^2 and multiply by 0.5 * 23.2.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.36 * 8.314 * 474 / 118.2.
Final: {"answer": 45.343, "unit": "kPa"}

Answer: 45.343

Prompt: An ideal gas sample has n=1.36 mol, T=474 K, and V=118.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.36 * 8.314 * 474 / 118.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1045 * 2.065 * 38.
Final: {"answer": 82001.15, "unit": "J"}

Answer: 82001.15

Prompt: A 1045 g sample has specific heat 2.065 J/(g*K). How much heat is needed to raise its temperature by 38 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1045 * 2.065 * 38.


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=139.4 V and R=134.8 ohm.
Final: {"answer": 144.157, "unit": "W"}

Answer: 144.157

Prompt: A resistor has resistance 134.8 ohm and voltage 139.4 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=139.4 V and R=134.8 ohm.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 9.1185, "unit": "state_units"}

Answer: 9.1185

Prompt: Use explicit Euler on dy/dt = -0.64 y with y(0)=29, step size h=0.5, for 3 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.
Apply that update for 3 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(8.7)=43.72 and f(10.2)=53.62.
3. The interval width is 1.5.
Final: {"answer": 73.005, "unit": "area_units"}

Answer: 73.005

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.6x+-13.7 from x=8.7 to x=10.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(8.7)=43.72 and f(10.2)=53.62.
The interval width is 1.5.


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=0.24 and add it to the current value.
Final: {"answer": [-0.336, -0.774, -0.026], "unit": "temperature_units"}

Answer: -0.336

Answer: -0.774

Answer: -0.026

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.35, right=3; current interior values are [0.0, -1.05, -0.95]. Use r=0.24. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=280 degrees and keep the unit as newtons.
Final: {"answer": [14.7601, -83.7087], "unit": "N"}

Answer: 14.7601

Answer: -83.7087

Prompt: A vector has magnitude 85 N at 280 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=280 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": [-1.65, -24.25], "unit": "dimensionless"}

Answer: -1.65

Answer: -24.25

Prompt: A line passes through points (17.25, -52.7125) and (30.5, -74.575). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In simulation spec case 417964, 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 running_total_007522(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_007522"}

Answer: python_code

Prompt: Write a Python function running_total_007522(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

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


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

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid warehouse survey records in release 218991, 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 = 5.9 kg and a = 7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 41.3, "unit": "N"}

Answer: 41.3

Prompt: A cart has mass 5.9 kg and measured acceleration 7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 5.9 kg and a = 7 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 8.7^2 and multiply by 0.5 * 12.5.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 473.0625, "unit": "J"}

Answer: 473.0625

Prompt: A body of mass 12.5 kg moves at 8.7 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 8.7^2 and multiply by 0.5 * 12.5.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=23 degrees through the sine of 2 theta.
3. Substitute v=56.4 m/s and g=9.81 m/s^2.
Final: {"answer": 233.2509, "unit": "m"}

Answer: 233.2509

Prompt: A projectile is launched on level ground with no air resistance at speed 56.4 m/s and angle 23 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=23 degrees through the sine of 2 theta.
Substitute v=56.4 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.26 * 8.314 * 419 / 64.4.
Final: {"answer": 122.2494, "unit": "kPa"}

Answer: 122.2494

Prompt: An ideal gas sample has n=2.26 mol, T=419 K, and V=64.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.26 * 8.314 * 419 / 64.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 965 * 1.075 * 28.
Final: {"answer": 29046.5, "unit": "J"}

Answer: 29046.5

Prompt: A 965 g sample has specific heat 1.075 J/(g*K). How much heat is needed to raise its temperature by 28 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 965 * 1.075 * 28.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=191.4 V and R=132 ohm.
Final: {"answer": 277.53, "unit": "W"}

Answer: 277.53

Prompt: A resistor has resistance 132 ohm and voltage 191.4 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=191.4 V and R=132 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=369 mg, t=277 h, and T_half=53.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 10.1958, "unit": "mg"}

Answer: 10.1958

Prompt: A radioactive sample starts with 369 mg. Its half-life is 53.5 hours. How many mg remain after 277 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=369 mg, t=277 h, and T_half=53.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 64.8007, "unit": "state_units"}

Answer: 64.8007

Prompt: Use explicit Euler on dy/dt = -0.08 y with y(0)=71.5, step size h=0.6, for 2 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.
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(9.5)=-3.25 and f(10.8)=-5.72.
3. The interval width is 1.3.
Final: {"answer": -5.8305, "unit": "area_units"}

Answer: -5.8305

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.9x+14.8 from x=9.5 to x=10.8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.5)=-3.25 and f(10.8)=-5.72.
The interval width is 1.3.


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=0.12 and add it to the current value.
Final: {"answer": [0.138, 0.482, 2.156], "unit": "temperature_units"}

Answer: 0.138

Answer: 0.482

Answer: 2.156

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, right=1.3; current interior values are [0.15, 0.2, 2.6]. 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 49.0 + 273.15.
Final: {"answer": 322.15, "unit": "K"}

Answer: 322.15

Prompt: Convert 49 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 49.0 + 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=340 degrees and keep the unit as newtons.
Final: {"answer": [107.5948, -39.1613], "unit": "N"}

Answer: 107.5948

Answer: -39.1613

Prompt: A vector has magnitude 114.5 N at 340 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=340 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": [5.7, 15.75], "unit": "dimensionless"}

Answer: 5.7

Answer: 15.75

Prompt: A line passes through points (4.75, 42.825) and (10, 72.75). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In student derivation case 859385, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def normalize_007540(values):
    total = sum(values)
    if total == 0:
        raise ValueError('cannot normalize zero-sum values')
    return [v / total for v in values]
```
Final: {"answer": "python_code", "function": "normalize_007540"}

Answer: python_code

Prompt: Write a Python function normalize_007540(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.

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

out = normalize_007540([2, 3, 5]); assert len(out) == 3

try:
    normalize_007540([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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)=56.5 and h=0.55, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 18 kg and a = 13 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 234.0, "unit": "N"}

Answer: 234.0

Prompt: A cart has mass 18 kg and measured acceleration 13 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 18 kg and a = 13 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 = 34.3^2 and multiply by 0.5 * 10.9.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 6411.8705, "unit": "J"}

Answer: 6411.8705

Prompt: A body of mass 10.9 kg moves at 34.3 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 34.3^2 and multiply by 0.5 * 10.9.
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=30 degrees through the sine of 2 theta.
3. Substitute v=18.6 m/s and g=9.81 m/s^2.
Final: {"answer": 30.5413, "unit": "m"}

Answer: 30.5413

Prompt: A projectile is launched on level ground with no air resistance at speed 18.6 m/s and angle 30 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=30 degrees through the sine of 2 theta.
Substitute v=18.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.77 * 8.314 * 329 / 48.5.
Final: {"answer": 269.0188, "unit": "kPa"}

Answer: 269.0188

Prompt: An ideal gas sample has n=4.77 mol, T=329 K, and V=48.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.77 * 8.314 * 329 / 48.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1085 * 0.53 * 31.
Final: {"answer": 17826.55, "unit": "J"}

Answer: 17826.55

Prompt: A 1085 g sample has specific heat 0.53 J/(g*K). How much heat is needed to raise its temperature by 31 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1085 * 0.53 * 31.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=236.7 V and R=73.3 ohm.
Final: {"answer": 764.3505, "unit": "W"}

Answer: 764.3505

Prompt: A resistor has resistance 73.3 ohm and voltage 236.7 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=236.7 V and R=73.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=946.5 mg, t=17.5 h, and T_half=33 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 655.3654, "unit": "mg"}

Answer: 655.3654

Prompt: A radioactive sample starts with 946.5 mg. Its half-life is 33 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=946.5 mg, t=17.5 h, and T_half=33 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.14 y, so each step multiplies y by 1 - h*0.14.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 2.4244, "unit": "state_units"}

Answer: 2.4244

Prompt: Use explicit Euler on dy/dt = -0.14 y with y(0)=4.5, step size h=1.9, for 2 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.14 y, so each step multiplies y by 1 - h*0.14.
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(-5.8)=48.54 and f(2.4)=5.08.
3. The interval width is 8.2.
Final: {"answer": 219.842, "unit": "area_units"}

Answer: 219.842

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.3x+17.8 from x=-5.8 to x=2.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-5.8)=48.54 and f(2.4)=5.08.
The interval width is 8.2.


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=0.16 and add it to the current value.
Final: {"answer": [-1.402, -0.396, -0.866], "unit": "temperature_units"}

Answer: -1.402

Answer: -0.396

Answer: -0.866

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.85, right=-0.2; current interior values are [-1.65, 0.1, -1.25]. Use r=0.16. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 109.5 + 273.15.
Final: {"answer": 382.65, "unit": "K"}

Answer: 382.65

Prompt: Convert 109.5 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 109.5 + 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=257 degrees and keep the unit as newtons.
Final: {"answer": [-68.9475, -298.6444], "unit": "N"}

Answer: -68.9475

Answer: -298.6444

Prompt: A vector has magnitude 306.5 N at 257 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=257 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": [7.1, 23.25], "unit": "dimensionless"}

Answer: 7.1

Answer: 23.25

Prompt: A line passes through points (-6.75, -24.675) and (7.5, 76.5). 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 simulation spec case 545439, 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 threshold_flags_007558(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_007558"}

Answer: python_code

Prompt: Write a Python function threshold_flags_007558(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.

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

assert threshold_flags_007558([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_007558([], 5) == []

assert threshold_flags_007558([-1, 0], 0) == [False, True]


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 37.55^2 and multiply by 0.5 * 2.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1938.7534, "unit": "J"}

Answer: 1938.7534

Prompt: A body of mass 2.75 kg moves at 37.55 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 37.55^2 and multiply by 0.5 * 2.75.
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 = 3.53 * 8.314 * 389 / 115.3.
Final: {"answer": 99.0159, "unit": "kPa"}

Answer: 99.0159

Prompt: An ideal gas sample has n=3.53 mol, T=389 K, and V=115.3 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 = 3.53 * 8.314 * 389 / 115.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 640 * 4.24 * 43.
Final: {"answer": 116684.8, "unit": "J"}

Answer: 116684.8

Prompt: A 640 g sample has specific heat 4.24 J/(g*K). How much heat is needed to raise its temperature by 43 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 640 * 4.24 * 43.


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=235.1 V and R=102.5 ohm.
Final: {"answer": 539.2391, "unit": "W"}

Answer: 539.2391

Prompt: A resistor has resistance 102.5 ohm and voltage 235.1 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=235.1 V and R=102.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=806 mg, t=243.5 h, and T_half=101.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 152.8128, "unit": "mg"}

Answer: 152.8128

Prompt: A radioactive sample starts with 806 mg. Its half-life is 101.5 hours. How many mg remain after 243.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=806 mg, t=243.5 h, and T_half=101.5 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 1040 mL to 1.04 L.
3. Compute M = 2.25 / 1.04.
Final: {"answer": 2.1635, "unit": "mol/L"}

Answer: 2.1635

Prompt: A solution contains 2.25 mol of solute in 1040 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1040 mL to 1.04 L.
Compute M = 2.25 / 1.04.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": -0.0107, "unit": "state_units"}

Answer: -0.0107

Prompt: Use explicit Euler on dy/dt = -0.59 y with y(0)=45, step size h=1.8, 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) = -0.59 y, so each step multiplies y by 1 - h*0.59.
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(3)=12.7 and f(5.9)=20.82.
3. The interval width is 2.9.
Final: {"answer": 48.604, "unit": "area_units"}

Answer: 48.604

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2.8x+4.3 from x=3 to x=5.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3)=12.7 and f(5.9)=20.82.
The interval width is 2.9.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4021.0 / 100.
Final: {"answer": 40.21, "unit": "m"}

Answer: 40.21

Prompt: Convert 4021 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 4021.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=94 degrees and keep the unit as newtons.
Final: {"answer": [-10.2891, 147.1407], "unit": "N"}

Answer: -10.2891

Answer: 147.1407

Prompt: A vector has magnitude 147.5 N at 94 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=94 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [9.45, -4.25], "unit": "dimensionless"}

Answer: 9.45

Answer: -4.25

Prompt: A line passes through points (-8.25, -82.2125) and (-0.75, -11.3375). 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 sensor calibration case 753975, 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 normalize_007576(values):
    total = sum(values)
    if total == 0:
        raise ValueError('cannot normalize zero-sum values')
    return [v / total for v in values]
```
Final: {"answer": "python_code", "function": "normalize_007576"}

Answer: python_code

Prompt: Write a Python function normalize_007576(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.

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

out = normalize_007576([2, 3, 5]); assert len(out) == 3

try:
    normalize_007576([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 33.1 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 1.25 kg and a = 5.7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 7.125, "unit": "N"}

Answer: 7.125

Prompt: A cart has mass 1.25 kg and measured acceleration 5.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 1.25 kg and a = 5.7 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 21.85^2 and multiply by 0.5 * 11.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2637.7593, "unit": "J"}

Answer: 2637.7593

Prompt: A body of mass 11.05 kg moves at 21.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 21.85^2 and multiply by 0.5 * 11.05.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=58 degrees through the sine of 2 theta.
3. Substitute v=12.8 m/s and g=9.81 m/s^2.
Final: {"answer": 15.0111, "unit": "m"}

Answer: 15.0111

Prompt: A projectile is launched on level ground with no air resistance at speed 12.8 m/s and angle 58 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=58 degrees through the sine of 2 theta.
Substitute v=12.8 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 = 5.34 * 8.314 * 498 / 38.7.
Final: {"answer": 571.3071, "unit": "kPa"}

Answer: 571.3071

Prompt: An ideal gas sample has n=5.34 mol, T=498 K, and V=38.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.34 * 8.314 * 498 / 38.7.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1695 * 1 * 73.
Final: {"answer": 123735.0, "unit": "J"}

Answer: 123735.0

Prompt: A 1695 g sample has specific heat 1 J/(g*K). How much heat is needed to raise its temperature by 73 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1695 * 1 * 73.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=34.2 V and R=137.2 ohm.
Final: {"answer": 8.5251, "unit": "W"}

Answer: 8.5251

Prompt: A resistor has resistance 137.2 ohm and voltage 34.2 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=34.2 V and R=137.2 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.65 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 265.2305, "unit": "g"}

Answer: 265.2305

Prompt: A sample contains 2.65 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 = 2.65 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 2005 mL to 2.005 L.
3. Compute M = 0.62 / 2.005.
Final: {"answer": 0.3092, "unit": "mol/L"}

Answer: 0.3092

Prompt: A solution contains 0.62 mol of solute in 2005 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2005 mL to 2.005 L.
Compute M = 0.62 / 2.005.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 6.483, "unit": "state_units"}

Answer: 6.483

Prompt: Use explicit Euler on dy/dt = -0.43 y with y(0)=19, step size h=0.45, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.
Apply that update for 5 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(4.7)=10.33 and f(5.5)=12.65.
3. The interval width is 0.8.
Final: {"answer": 9.192, "unit": "area_units"}

Answer: 9.192

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2.9x+-3.3 from x=4.7 to x=5.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.7)=10.33 and f(5.5)=12.65.
The interval width is 0.8.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.44 and add it to the current value.
Final: {"answer": [-0.754, 1.468, 0.598], "unit": "temperature_units"}

Answer: -0.754

Answer: 1.468

Answer: 0.598

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1, right=1.95; current interior values are [1.6, -1.15, 2.05]. 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. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=355 degrees and keep the unit as newtons.
Final: {"answer": [112.0719, -9.805], "unit": "N"}

Answer: 112.0719

Answer: -9.805

Prompt: A vector has magnitude 112.5 N at 355 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=355 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-6.15, 24.75], "unit": "dimensionless"}

Answer: -6.15

Answer: 24.75

Prompt: A line passes through points (-3.75, 47.8125) and (4, 0.15). Return [slope, intercept] for y = slope*x + intercept.

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