Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=79.2 V and R=22.9 ohm.
Final: {"answer": 273.9144, "unit": "W"}

Answer: 273.9144

Prompt: A resistor has resistance 22.9 ohm and voltage 79.2 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=79.2 V and R=22.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=511.5 mg, t=56.5 h, and T_half=35.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 169.7233, "unit": "mg"}

Answer: 169.7233

Prompt: A radioactive sample starts with 511.5 mg. Its half-life is 35.5 hours. How many mg remain after 56.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=511.5 mg, t=56.5 h, and T_half=35.5 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 = 2.58 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 258.2245, "unit": "g"}

Answer: 258.2245

Prompt: A sample contains 2.58 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 = 2.58 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 2265 mL to 2.265 L.
3. Compute M = 4.31 / 2.265.
Final: {"answer": 1.9029, "unit": "mol/L"}

Answer: 1.9029

Prompt: A solution contains 4.31 mol of solute in 2265 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2265 mL to 2.265 L.
Compute M = 4.31 / 2.265.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.5887, "unit": "state_units"}

Answer: 0.5887

Prompt: Use explicit Euler on dy/dt = -0.41 y with y(0)=21.5, step size h=1.1, for 6 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-1.9)=12.03 and f(1.7)=-15.69.
3. The interval width is 3.6.
Final: {"answer": -6.588, "unit": "area_units"}

Answer: -6.588

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.7x+-2.6 from x=-1.9 to x=1.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-1.9)=12.03 and f(1.7)=-15.69.
The interval width is 3.6.

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


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.4 and add it to the current value.
Final: {"answer": [-1.01, -0.6, -0.13], "unit": "temperature_units"}

Answer: -1.01

Answer: -0.6

Answer: -0.13

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.85, right=-0.25; current interior values are [-1.35, 0.0, -0.15]. Use r=0.4. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=149 degrees and keep the unit as newtons.
Final: {"answer": [-9.0003, 5.4079], "unit": "N"}

Answer: -9.0003

Answer: 5.4079

Prompt: A vector has magnitude 10.5 N at 149 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=149 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": [-6.85, -24.5], "unit": "dimensionless"}

Answer: -6.85

Answer: -24.5

Prompt: A line passes through points (5.5, -62.175) and (19, -154.65). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In instrument manual case 45398, 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. Use Newton's second law F = m a.
2. Substitute m = 16.1 kg and a = 13.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 218.155, "unit": "N"}

Answer: 218.155

Prompt: A cart has mass 16.1 kg and measured acceleration 13.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 16.1 kg and a = 13.55 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 32.35^2 and multiply by 0.5 * 27.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 14154.2168, "unit": "J"}

Answer: 14154.2168

Prompt: A body of mass 27.05 kg moves at 32.35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 32.35^2 and multiply by 0.5 * 27.05.
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=50 degrees through the sine of 2 theta.
3. Substitute v=31 m/s and g=9.81 m/s^2.
Final: {"answer": 96.473, "unit": "m"}

Answer: 96.473

Prompt: A projectile is launched on level ground with no air resistance at speed 31 m/s and angle 50 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=50 degrees through the sine of 2 theta.
Substitute v=31 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 = 3.02 * 8.314 * 530 / 65.8.
Final: {"answer": 202.2399, "unit": "kPa"}

Answer: 202.2399

Prompt: An ideal gas sample has n=3.02 mol, T=530 K, and V=65.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.02 * 8.314 * 530 / 65.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 890 * 3.125 * 16.
Final: {"answer": 44500.0, "unit": "J"}

Answer: 44500.0

Prompt: A 890 g sample has specific heat 3.125 J/(g*K). How much heat is needed to raise its temperature by 16 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 890 * 3.125 * 16.


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=141.2 V and R=57.5 ohm.
Final: {"answer": 346.7381, "unit": "W"}

Answer: 346.7381

Prompt: A resistor has resistance 57.5 ohm and voltage 141.2 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=141.2 V and R=57.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=433.5 mg, t=3 h, and T_half=92.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 423.8634, "unit": "mg"}

Answer: 423.8634

Prompt: A radioactive sample starts with 433.5 mg. Its half-life is 92.5 hours. How many mg remain after 3 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=433.5 mg, t=3 h, and T_half=92.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.51 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 286.5051, "unit": "g"}

Answer: 286.5051

Prompt: A sample contains 6.51 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.51 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 8.2298, "unit": "state_units"}

Answer: 8.2298

Prompt: Use explicit Euler on dy/dt = -0.17 y with y(0)=28.5, step size h=1.1, for 6 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(7.3)=28.39 and f(15.7)=81.31.
3. The interval width is 8.4.
Final: {"answer": 460.74, "unit": "area_units"}

Answer: 460.74

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.3x+-17.6 from x=7.3 to x=15.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7.3)=28.39 and f(15.7)=81.31.
The interval width is 8.4.


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=0.04 and add it to the current value.
Final: {"answer": [-0.734, 0.566, 2.164], "unit": "temperature_units"}

Answer: -0.734

Answer: 0.566

Answer: 2.164

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.65, right=1.8; current interior values are [-0.75, 0.55, 2.25]. Use r=0.04. 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=0.04 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 19360.0 / 1000.
Final: {"answer": 19.36, "unit": "kg"}

Answer: 19.36

Prompt: Convert 19360 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 19360.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=210 degrees and keep the unit as newtons.
Final: {"answer": [-153.7195, -88.75], "unit": "N"}

Answer: -153.7195

Answer: -88.75

Prompt: A vector has magnitude 177.5 N at 210 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=210 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": [2.1, 28.75], "unit": "dimensionless"}

Answer: 2.1

Answer: 28.75

Prompt: A line passes through points (19.75, 70.225) and (28, 87.55). 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 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 sensor calibration case 96329, 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 threshold_flags_004912(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_004912"}

Answer: python_code

Prompt: Write a Python function threshold_flags_004912(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_004912([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_004912([], 5) == []

assert threshold_flags_004912([-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: 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 42.5 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 5.6 kg and a = 14.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 80.08, "unit": "N"}

Answer: 80.08

Prompt: A cart has mass 5.6 kg and measured acceleration 14.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 5.6 kg and a = 14.3 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 23.25^2 and multiply by 0.5 * 16.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 4378.5562, "unit": "J"}

Answer: 4378.5562

Prompt: A body of mass 16.2 kg moves at 23.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 23.25^2 and multiply by 0.5 * 16.2.
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 = 3.2 * 8.314 * 268 / 22.1.
Final: {"answer": 322.6283, "unit": "kPa"}

Answer: 322.6283

Prompt: An ideal gas sample has n=3.2 mol, T=268 K, and V=22.1 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 = 3.2 * 8.314 * 268 / 22.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 405 * 4.28 * 73.
Final: {"answer": 126538.2, "unit": "J"}

Answer: 126538.2

Prompt: A 405 g sample has specific heat 4.28 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 = 405 * 4.28 * 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=237.6 V and R=135.2 ohm.
Final: {"answer": 417.5574, "unit": "W"}

Answer: 417.5574

Prompt: A resistor has resistance 135.2 ohm and voltage 237.6 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=237.6 V and R=135.2 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=73.5 mg, t=293 h, and T_half=46 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.8889, "unit": "mg"}

Answer: 0.8889

Prompt: A radioactive sample starts with 73.5 mg. Its half-life is 46 hours. How many mg remain after 293 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=73.5 mg, t=293 h, and T_half=46 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 = 0.34 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 6.1251, "unit": "g"}

Answer: 6.1251

Prompt: A sample contains 0.34 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.34 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2960 mL to 2.96 L.
3. Compute M = 1.85 / 2.96.
Final: {"answer": 0.625, "unit": "mol/L"}

Answer: 0.625

Prompt: A solution contains 1.85 mol of solute in 2960 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2960 mL to 2.96 L.
Compute M = 1.85 / 2.96.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(7.5)=-8.5 and f(14.4)=-5.74.
3. The interval width is 6.9.
Final: {"answer": -49.128, "unit": "area_units"}

Answer: -49.128

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.4x+-11.5 from x=7.5 to x=14.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7.5)=-8.5 and f(14.4)=-5.74.
The interval width is 6.9.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.1 and add it to the current value.
Final: {"answer": [0.785, 0.755, 1.32], "unit": "temperature_units"}

Answer: 0.785

Answer: 0.755

Answer: 1.32

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=1.55, right=2.5; current interior values are [0.7, 0.7, 1.25]. Use r=0.1. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 192.0 + 273.15.
Final: {"answer": 465.15, "unit": "K"}

Answer: 465.15

Prompt: Convert 192 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 192.0 + 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=182 degrees and keep the unit as newtons.
Final: {"answer": [-268.3364, -9.3705], "unit": "N"}

Answer: -268.3364

Answer: -9.3705

Prompt: A vector has magnitude 268.5 N at 182 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=182 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [3.75, -18.5], "unit": "dimensionless"}

Answer: 3.75

Answer: -18.5

Prompt: A line passes through points (-5, -37.25) and (7.75, 10.5625). 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 times time gives distance, not acceleration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In instrument manual case 733265, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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=0.22 and interior values [-1.85, -1.3, -0.25], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 3.9 kg and a = 2.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 8.775, "unit": "N"}

Answer: 8.775

Prompt: A cart has mass 3.9 kg and measured acceleration 2.25 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 = 3.9 kg and a = 2.25 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 = 15.7^2 and multiply by 0.5 * 4.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 579.2515, "unit": "J"}

Answer: 579.2515

Prompt: A body of mass 4.7 kg moves at 15.7 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 15.7^2 and multiply by 0.5 * 4.7.
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=16 degrees through the sine of 2 theta.
3. Substitute v=66 m/s and g=9.81 m/s^2.
Final: {"answer": 235.3036, "unit": "m"}

Answer: 235.3036

Prompt: A projectile is launched on level ground with no air resistance at speed 66 m/s and angle 16 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=16 degrees through the sine of 2 theta.
Substitute v=66 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 = 5.09 * 8.314 * 474 / 114.5.
Final: {"answer": 175.1865, "unit": "kPa"}

Answer: 175.1865

Prompt: An ideal gas sample has n=5.09 mol, T=474 K, and V=114.5 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 = 5.09 * 8.314 * 474 / 114.5.


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=185.6 V and R=83.4 ohm.
Final: {"answer": 413.0379, "unit": "W"}

Answer: 413.0379

Prompt: A resistor has resistance 83.4 ohm and voltage 185.6 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=185.6 V and R=83.4 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.8 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 80.0696, "unit": "g"}

Answer: 80.0696

Prompt: A sample contains 0.8 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.8 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.07 y, so each step multiplies y by 1 - h*0.07.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 15.6567, "unit": "state_units"}

Answer: 15.6567

Prompt: Use explicit Euler on dy/dt = -0.07 y with y(0)=29.5, step size h=1.7, 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) = -0.07 y, so each step multiplies y by 1 - h*0.07.
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(-3)=-4.9 and f(3)=18.5.
3. The interval width is 6.
Final: {"answer": 40.8, "unit": "area_units"}

Answer: 40.8

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.9x+6.8 from x=-3 to x=3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-3)=-4.9 and f(3)=18.5.
The interval width is 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=0.3 and add it to the current value.
Final: {"answer": [0.385, 0.87, 0.495], "unit": "temperature_units"}

Answer: 0.385

Answer: 0.87

Answer: 0.495

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.6, right=-0.9; current interior values are [-0.5, 2.55, 0.0]. Use r=0.3. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4628.5 / 100.
Final: {"answer": 46.285, "unit": "m"}

Answer: 46.285

Prompt: Convert 4628.5 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 4628.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=85 degrees and keep the unit as newtons.
Final: {"answer": [2.1789, 24.9049], "unit": "N"}

Answer: 2.1789

Answer: 24.9049

Prompt: A vector has magnitude 25 N at 85 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=85 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-4.95, 16.75], "unit": "dimensionless"}

Answer: -4.95

Answer: 16.75

Prompt: A line passes through points (-6.5, 48.925) and (-1, 21.7). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. 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 quality-control check case 123424, 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 threshold_flags_004948(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_004948"}

Answer: python_code

Prompt: Write a Python function threshold_flags_004948(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_004948([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_004948([], 5) == []

assert threshold_flags_004948([-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: 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 67 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 10.1 kg and a = 13.7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 138.37, "unit": "N"}

Answer: 138.37

Prompt: A cart has mass 10.1 kg and measured acceleration 13.7 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 = 10.1 kg and a = 13.7 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 = 3.45^2 and multiply by 0.5 * 24.25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 144.3178, "unit": "J"}

Answer: 144.3178

Prompt: A body of mass 24.25 kg moves at 3.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 3.45^2 and multiply by 0.5 * 24.25.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=65 degrees through the sine of 2 theta.
3. Substitute v=69.8 m/s and g=9.81 m/s^2.
Final: {"answer": 380.4484, "unit": "m"}

Answer: 380.4484

Prompt: A projectile is launched on level ground with no air resistance at speed 69.8 m/s and angle 65 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=65 degrees through the sine of 2 theta.
Substitute v=69.8 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 = 0.18 * 8.314 * 546 / 35.6.
Final: {"answer": 22.9522, "unit": "kPa"}

Answer: 22.9522

Prompt: An ideal gas sample has n=0.18 mol, T=546 K, and V=35.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.18 * 8.314 * 546 / 35.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1435 * 2.51 * 19.
Final: {"answer": 68435.15, "unit": "J"}

Answer: 68435.15

Prompt: A 1435 g sample has specific heat 2.51 J/(g*K). How much heat is needed to raise its temperature by 19 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1435 * 2.51 * 19.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=162.8 V and R=19.3 ohm.
Final: {"answer": 1373.256, "unit": "W"}

Answer: 1373.256

Prompt: A resistor has resistance 19.3 ohm and voltage 162.8 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=162.8 V and R=19.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=793 mg, t=334.5 h, and T_half=27.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.1728, "unit": "mg"}

Answer: 0.1728

Prompt: A radioactive sample starts with 793 mg. Its half-life is 27.5 hours. How many mg remain after 334.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=793 mg, t=334.5 h, and T_half=27.5 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 = 0.25 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 4.5038, "unit": "g"}

Answer: 4.5038

Prompt: A sample contains 0.25 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.25 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1460 mL to 1.46 L.
3. Compute M = 1.075 / 1.46.
Final: {"answer": 0.7363, "unit": "mol/L"}

Answer: 0.7363

Prompt: A solution contains 1.075 mol of solute in 1460 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1460 mL to 1.46 L.
Compute M = 1.075 / 1.46.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.212, "unit": "state_units"}

Answer: 0.212

Prompt: Use explicit Euler on dy/dt = -0.21 y with y(0)=29, step size h=1.85, for 10 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.5)=5.3 and f(12.2)=4.76.
3. The interval width is 2.7.
Final: {"answer": 13.581, "unit": "area_units"}

Answer: 13.581

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.2x+7.2 from x=9.5 to x=12.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.5)=5.3 and f(12.2)=4.76.
The interval width is 2.7.


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=0.22 and add it to the current value.
Final: {"answer": [-0.557, 0.781, 1.23], "unit": "temperature_units"}

Answer: -0.557

Answer: 0.781

Answer: 1.23

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=0.8; current interior values are [-0.7, 1.1, 1.45]. Use r=0.22. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 40467.0 / 1000.
Final: {"answer": 40.467, "unit": "kg"}

Answer: 40.467

Prompt: Convert 40467 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 40467.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=306 degrees and keep the unit as newtons.
Final: {"answer": [28.2137, -38.8328], "unit": "N"}

Answer: 28.2137

Answer: -38.8328

Prompt: A vector has magnitude 48 N at 306 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=306 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-0.5, 21.25], "unit": "dimensionless"}

Answer: -0.5

Answer: 21.25

Prompt: A line passes through points (-4, 23.25) and (0.25, 21.125). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In simulation spec case 301797, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def safe_mean_004966(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_004966"}

Answer: python_code

Prompt: Write a Python function safe_mean_004966(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_004966([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 6.2 kg and a = 12.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 75.02, "unit": "N"}

Answer: 75.02

Prompt: A cart has mass 6.2 kg and measured acceleration 12.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 6.2 kg and a = 12.1 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 29.2^2 and multiply by 0.5 * 11.4.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 4860.048, "unit": "J"}

Answer: 4860.048

Prompt: A body of mass 11.4 kg moves at 29.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 29.2^2 and multiply by 0.5 * 11.4.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=65 degrees through the sine of 2 theta.
3. Substitute v=43.1 m/s and g=9.81 m/s^2.
Final: {"answer": 145.0573, "unit": "m"}

Answer: 145.0573

Prompt: A projectile is launched on level ground with no air resistance at speed 43.1 m/s and angle 65 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=65 degrees through the sine of 2 theta.
Substitute v=43.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.42 * 8.314 * 465 / 91.1.
Final: {"answer": 17.8235, "unit": "kPa"}

Answer: 17.8235

Prompt: An ideal gas sample has n=0.42 mol, T=465 K, and V=91.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.42 * 8.314 * 465 / 91.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1960 * 4.58 * 39.
Final: {"answer": 350095.2, "unit": "J"}

Answer: 350095.2

Prompt: A 1960 g sample has specific heat 4.58 J/(g*K). How much heat is needed to raise its temperature by 39 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1960 * 4.58 * 39.


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=135.1 V and R=100.9 ohm.
Final: {"answer": 180.8921, "unit": "W"}

Answer: 180.8921

Prompt: A resistor has resistance 100.9 ohm and voltage 135.1 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=135.1 V and R=100.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=796.5 mg, t=359.5 h, and T_half=84 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 41.0062, "unit": "mg"}

Answer: 41.0062

Prompt: A radioactive sample starts with 796.5 mg. Its half-life is 84 hours. How many mg remain after 359.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=796.5 mg, t=359.5 h, and T_half=84 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.46 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 803.4958, "unit": "g"}

Answer: 803.4958

Prompt: A sample contains 4.46 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.46 mol * 180.156 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(-0.6)=-1.66 and f(7.4)=11.14.
3. The interval width is 8.
Final: {"answer": 37.92, "unit": "area_units"}

Answer: 37.92

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.6x+-0.7 from x=-0.6 to x=7.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-0.6)=-1.66 and f(7.4)=11.14.
The interval width is 8.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 131.5 + 273.15.
Final: {"answer": 404.65, "unit": "K"}

Answer: 404.65

Prompt: Convert 131.5 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 131.5 + 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=194 degrees and keep the unit as newtons.
Final: {"answer": [-208.1284, -51.8922], "unit": "N"}

Answer: -208.1284

Answer: -51.8922

Prompt: A vector has magnitude 214.5 N at 194 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=194 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": [-5.8, -22.25], "unit": "dimensionless"}

Answer: -5.8

Answer: -22.25

Prompt: A line passes through points (-11, 41.55) and (-2.75, -6.3). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In quality-control check case 914390, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 2 kg and a = 2.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 5.7, "unit": "N"}

Answer: 5.7

Prompt: A cart has mass 2 kg and measured acceleration 2.85 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 = 2 kg and a = 2.85 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 = 17.15^2 and multiply by 0.5 * 28.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 4205.9517, "unit": "J"}

Answer: 4205.9517

Prompt: A body of mass 28.6 kg moves at 17.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 17.15^2 and multiply by 0.5 * 28.6.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.92 * 8.314 * 305 / 13.6.
Final: {"answer": 917.3521, "unit": "kPa"}

Answer: 917.3521

Prompt: An ideal gas sample has n=4.92 mol, T=305 K, and V=13.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.92 * 8.314 * 305 / 13.6.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 745 * 1.17 * 31.
Final: {"answer": 27021.15, "unit": "J"}

Answer: 27021.15

Prompt: A 745 g sample has specific heat 1.17 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 = 745 * 1.17 * 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=176.9 V and R=136.5 ohm.
Final: {"answer": 229.2572, "unit": "W"}

Answer: 229.2572

Prompt: A resistor has resistance 136.5 ohm and voltage 176.9 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=176.9 V and R=136.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=794 mg, t=255 h, and T_half=97 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 128.3669, "unit": "mg"}

Answer: 128.3669

Prompt: A radioactive sample starts with 794 mg. Its half-life is 97 hours. How many mg remain after 255 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=794 mg, t=255 h, and T_half=97 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 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 44.01, "unit": "g"}

Answer: 44.01

Prompt: A sample contains 1 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(4.2)=22.56 and f(10.3)=70.14.
3. The interval width is 6.1.
Final: {"answer": 282.735, "unit": "area_units"}

Answer: 282.735

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.8x+-10.2 from x=4.2 to x=10.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.2)=22.56 and f(10.3)=70.14.
The interval width is 6.1.


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=0.44 and add it to the current value.
Final: {"answer": [0.7, 1.622, -0.34], "unit": "temperature_units"}

Answer: 0.7

Answer: 1.622

Answer: -0.34

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.6, right=-1.75; current interior values are [1.8, 0.5, 1.75]. 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=300 degrees and keep the unit as newtons.
Final: {"answer": [41.0, -71.0141], "unit": "N"}

Answer: 41.0

Answer: -71.0141

Prompt: A vector has magnitude 82 N at 300 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=300 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [0.95, -16.25], "unit": "dimensionless"}

Answer: 0.95

Answer: -16.25

Prompt: A line passes through points (16, -1.05) and (23.5, 6.075). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In quality-control check case 340462, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def clamp_005002(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_005002"}

Answer: python_code

Prompt: Write a Python function clamp_005002(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.

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

try:
    clamp_005002(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 24.2 kg and a = 9.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 229.9, "unit": "N"}

Answer: 229.9

Prompt: A cart has mass 24.2 kg and measured acceleration 9.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 24.2 kg and a = 9.5 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 = 40.1^2 and multiply by 0.5 * 26.1.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 20984.5305, "unit": "J"}

Answer: 20984.5305

Prompt: A body of mass 26.1 kg moves at 40.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 40.1^2 and multiply by 0.5 * 26.1.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=84 degrees through the sine of 2 theta.
3. Substitute v=7.2 m/s and g=9.81 m/s^2.
Final: {"answer": 1.0987, "unit": "m"}

Answer: 1.0987

Prompt: A projectile is launched on level ground with no air resistance at speed 7.2 m/s and angle 84 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=84 degrees through the sine of 2 theta.
Substitute v=7.2 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 = 1975 * 2.92 * 87.
Final: {"answer": 501729.0, "unit": "J"}

Answer: 501729.0

Prompt: A 1975 g sample has specific heat 2.92 J/(g*K). How much heat is needed to raise its temperature by 87 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1975 * 2.92 * 87.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=200.2 V and R=155.8 ohm.
Final: {"answer": 257.2531, "unit": "W"}

Answer: 257.2531

Prompt: A resistor has resistance 155.8 ohm and voltage 200.2 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=200.2 V and R=155.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=809.5 mg, t=110 h, and T_half=101.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 381.9244, "unit": "mg"}

Answer: 381.9244

Prompt: A radioactive sample starts with 809.5 mg. Its half-life is 101.5 hours. How many mg remain after 110 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=809.5 mg, t=110 h, and T_half=101.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.35 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 423.3666, "unit": "g"}

Answer: 423.3666

Prompt: A sample contains 2.35 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 = 2.35 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 1910 mL to 1.91 L.
3. Compute M = 0.22 / 1.91.
Final: {"answer": 0.1152, "unit": "mol/L"}

Answer: 0.1152

Prompt: A solution contains 0.22 mol of solute in 1910 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1910 mL to 1.91 L.
Compute M = 0.22 / 1.91.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.05 y, so each step multiplies y by 1 - h*0.05.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 30.2331, "unit": "state_units"}

Answer: 30.2331

Prompt: Use explicit Euler on dy/dt = -0.05 y with y(0)=46.5, step size h=1.65, 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) = -0.05 y, so each step multiplies y by 1 - h*0.05.
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(1.4)=6.4 and f(2.4)=4.9.
3. The interval width is 1.
Final: {"answer": 5.65, "unit": "area_units"}

Answer: 5.65

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.5x+8.5 from x=1.4 to x=2.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.4)=6.4 and f(2.4)=4.9.
The interval width is 1.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 133.0 + 273.15.
Final: {"answer": 406.15, "unit": "K"}

Answer: 406.15

Prompt: Convert 133 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 133.0 + 273.15.


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

Answer: consistent

Prompt: In simulation spec case 467480, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def running_total_005020(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_005020"}

Answer: python_code

Prompt: Write a Python function running_total_005020(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: 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=2.47 mol and T=518 K, but does not give volume. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 5.55 kg and a = 14.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 80.475, "unit": "N"}

Answer: 80.475

Prompt: A cart has mass 5.55 kg and measured acceleration 14.5 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 = 5.55 kg and a = 14.5 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 23.5^2 and multiply by 0.5 * 5.4.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1491.075, "unit": "J"}

Answer: 1491.075

Prompt: A body of mass 5.4 kg moves at 23.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 23.5^2 and multiply by 0.5 * 5.4.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=51 degrees through the sine of 2 theta.
3. Substitute v=23.6 m/s and g=9.81 m/s^2.
Final: {"answer": 55.5341, "unit": "m"}

Answer: 55.5341

Prompt: A projectile is launched on level ground with no air resistance at speed 23.6 m/s and angle 51 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=51 degrees through the sine of 2 theta.
Substitute v=23.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.93 * 8.314 * 309 / 3.1.
Final: {"answer": 4914.2981, "unit": "kPa"}

Answer: 4914.2981

Prompt: An ideal gas sample has n=5.93 mol, T=309 K, and V=3.1 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 = 5.93 * 8.314 * 309 / 3.1.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=216.6 V and R=18.2 ohm.
Final: {"answer": 2577.778, "unit": "W"}

Answer: 2577.778

Prompt: A resistor has resistance 18.2 ohm and voltage 216.6 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=216.6 V and R=18.2 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.93 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 527.8571, "unit": "g"}

Answer: 527.8571

Prompt: A sample contains 2.93 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 = 2.93 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 2070 mL to 2.07 L.
3. Compute M = 1.305 / 2.07.
Final: {"answer": 0.6304, "unit": "mol/L"}

Answer: 0.6304

Prompt: A solution contains 1.305 mol of solute in 2070 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2070 mL to 2.07 L.
Compute M = 1.305 / 2.07.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 5.5949, "unit": "state_units"}

Answer: 5.5949

Prompt: Use explicit Euler on dy/dt = -0.41 y with y(0)=7.5, step size h=0.1, 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) = -0.41 y, so each step multiplies y by 1 - h*0.41.
Apply that update for 7 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6.7)=10.76 and f(-6.5)=10.2.
3. The interval width is 0.2.
Final: {"answer": 2.096, "unit": "area_units"}

Answer: 2.096

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.8x+-8 from x=-6.7 to x=-6.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.7)=10.76 and f(-6.5)=10.2.
The interval width is 0.2.


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=0.04 and add it to the current value.
Final: {"answer": [-1.186, 0.644, 1.152], "unit": "temperature_units"}

Answer: -1.186

Answer: 0.644

Answer: 1.152

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.45, right=-1.8; current interior values are [-1.3, 0.7, 1.3]. Use r=0.04. 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=0.04 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 142.0 + 273.15.
Final: {"answer": 415.15, "unit": "K"}

Answer: 415.15

Prompt: Convert 142 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 142.0 + 273.15.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-1.6, 11.25], "unit": "dimensionless"}

Answer: -1.6

Answer: 11.25

Prompt: A line passes through points (16, -14.35) and (19, -19.15). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. 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 lab notebook case 313709, 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_005038(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_005038"}

Answer: python_code

Prompt: Write a Python function threshold_flags_005038(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_005038([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_005038([], 5) == []

assert threshold_flags_005038([-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: required_fields, allowed_transformations.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid billing crop records in release 676777, 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 = 10.1 kg and a = 14.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 147.965, "unit": "N"}

Answer: 147.965

Prompt: A cart has mass 10.1 kg and measured acceleration 14.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 10.1 kg and a = 14.65 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 35.8^2 and multiply by 0.5 * 2.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1762.255, "unit": "J"}

Answer: 1762.255

Prompt: A body of mass 2.75 kg moves at 35.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 35.8^2 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 = 2.01 * 8.314 * 303 / 42.8.
Final: {"answer": 118.3055, "unit": "kPa"}

Answer: 118.3055

Prompt: An ideal gas sample has n=2.01 mol, T=303 K, and V=42.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.01 * 8.314 * 303 / 42.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1195 * 2.115 * 79.
Final: {"answer": 199666.575, "unit": "J"}

Answer: 199666.575

Prompt: A 1195 g sample has specific heat 2.115 J/(g*K). How much heat is needed to raise its temperature by 79 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1195 * 2.115 * 79.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=280.5 mg, t=113 h, and T_half=65.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 84.8396, "unit": "mg"}

Answer: 84.8396

Prompt: A radioactive sample starts with 280.5 mg. Its half-life is 65.5 hours. How many mg remain after 113 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=280.5 mg, t=113 h, and T_half=65.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.81 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 281.0964, "unit": "g"}

Answer: 281.0964

Prompt: A sample contains 4.81 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 = 4.81 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2175 mL to 2.175 L.
3. Compute M = 1.46 / 2.175.
Final: {"answer": 0.6713, "unit": "mol/L"}

Answer: 0.6713

Prompt: A solution contains 1.46 mol of solute in 2175 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2175 mL to 2.175 L.
Compute M = 1.46 / 2.175.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.05 y, so each step multiplies y by 1 - h*0.05.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 9.6553, "unit": "state_units"}

Answer: 9.6553

Prompt: Use explicit Euler on dy/dt = -0.05 y with y(0)=17, step size h=1.1, for 10 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.05 y, so each step multiplies y by 1 - h*0.05.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.4)=62.28 and f(19.1)=132.12.
3. The interval width is 9.7.
Final: {"answer": 942.84, "unit": "area_units"}

Answer: 942.84

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.2x+-5.4 from x=9.4 to x=19.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.4)=62.28 and f(19.1)=132.12.
The interval width is 9.7.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.22 and add it to the current value.
Final: {"answer": [-0.641, 1.366, 1.698], "unit": "temperature_units"}

Answer: -0.641

Answer: 1.366

Answer: 1.698

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=-1.75, right=1.5; current interior values are [-1.4, 2.4, 1.5]. Use r=0.22. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 9388.0 / 1000.
Final: {"answer": 9.388, "unit": "kg"}

Answer: 9.388

Prompt: Convert 9388 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 9388.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=115 degrees and keep the unit as newtons.
Final: {"answer": [-192.9252, 413.7295], "unit": "N"}

Answer: -192.9252

Answer: 413.7295

Prompt: A vector has magnitude 456.5 N at 115 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=115 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 model card equation case 147153, 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 billing sensor record from batch 327655 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 = 2.25 kg and a = 11.05 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 24.8625, "unit": "N"}

Answer: 24.8625

Prompt: A cart has mass 2.25 kg and measured acceleration 11.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 2.25 kg and a = 11.05 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=6 degrees through the sine of 2 theta.
3. Substitute v=61.3 m/s and g=9.81 m/s^2.
Final: {"answer": 79.6399, "unit": "m"}

Answer: 79.6399

Prompt: A projectile is launched on level ground with no air resistance at speed 61.3 m/s and angle 6 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=6 degrees through the sine of 2 theta.
Substitute v=61.3 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.56 * 8.314 * 400 / 109.0.
Final: {"answer": 108.6159, "unit": "kPa"}

Answer: 108.6159

Prompt: An ideal gas sample has n=3.56 mol, T=400 K, and V=109.0 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 = 3.56 * 8.314 * 400 / 109.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 620 * 4.74 * 111.
Final: {"answer": 326206.8, "unit": "J"}

Answer: 326206.8

Prompt: A 620 g sample has specific heat 4.74 J/(g*K). How much heat is needed to raise its temperature by 111 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 620 * 4.74 * 111.


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=174.1 V and R=99.5 ohm.
Final: {"answer": 304.6313, "unit": "W"}

Answer: 304.6313

Prompt: A resistor has resistance 99.5 ohm and voltage 174.1 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=174.1 V and R=99.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=910.5 mg, t=90.5 h, and T_half=4 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0001, "unit": "mg"}

Answer: 0.0001

Prompt: A radioactive sample starts with 910.5 mg. Its half-life is 4 hours. How many mg remain after 90.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=910.5 mg, t=90.5 h, and T_half=4 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 = 1.6 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 70.416, "unit": "g"}

Answer: 70.416

Prompt: A sample contains 1.6 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.6 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 4760 mL to 4.76 L.
3. Compute M = 1.805 / 4.76.
Final: {"answer": 0.3792, "unit": "mol/L"}

Answer: 0.3792

Prompt: A solution contains 1.805 mol of solute in 4760 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4760 mL to 4.76 L.
Compute M = 1.805 / 4.76.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.65 y, so each step multiplies y by 1 - h*0.65.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 32.7864, "unit": "state_units"}

Answer: 32.7864

Prompt: Use explicit Euler on dy/dt = -0.65 y with y(0)=65.5, step size h=0.45, 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) = -0.65 y, so each step multiplies y by 1 - h*0.65.
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(-3.7)=32.66 and f(5.4)=-38.32.
3. The interval width is 9.1.
Final: {"answer": -25.753, "unit": "area_units"}

Answer: -25.753

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.8x+3.8 from x=-3.7 to x=5.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-3.7)=32.66 and f(5.4)=-38.32.
The interval width is 9.1.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.4 and add it to the current value.
Final: {"answer": [0.51, -0.66, -1.8], "unit": "temperature_units"}

Answer: 0.51

Answer: -0.66

Answer: -1.8

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.7, right=-1.95; current interior values are [0.75, -1.8, -1.5]. Use r=0.4. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 36.5 + 273.15.
Final: {"answer": 309.65, "unit": "K"}

Answer: 309.65

Prompt: Convert 36.5 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 36.5 + 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=47 degrees and keep the unit as newtons.
Final: {"answer": [162.3156, 174.0622], "unit": "N"}

Answer: 162.3156

Answer: 174.0622

Prompt: A vector has magnitude 238 N at 47 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=47 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [0.05, -1.0], "unit": "dimensionless"}

Answer: 0.05

Answer: -1.0

Prompt: A line passes through points (-1.75, -1.0875) and (-1.25, -1.0625). 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 lab notebook case 181073, 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. 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=5.86 mol and T=571 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 = 6.35 kg and a = 2.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 17.4625, "unit": "N"}

Answer: 17.4625

Prompt: A cart has mass 6.35 kg and measured acceleration 2.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 6.35 kg and a = 2.75 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 9.75^2 and multiply by 0.5 * 12.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 598.8937, "unit": "J"}

Answer: 598.8937

Prompt: A body of mass 12.6 kg moves at 9.75 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 9.75^2 and multiply by 0.5 * 12.6.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=27 degrees through the sine of 2 theta.
3. Substitute v=63.3 m/s and g=9.81 m/s^2.
Final: {"answer": 330.4426, "unit": "m"}

Answer: 330.4426

Prompt: A projectile is launched on level ground with no air resistance at speed 63.3 m/s and angle 27 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=27 degrees through the sine of 2 theta.
Substitute v=63.3 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.72 * 8.314 * 272 / 52.8.
Final: {"answer": 73.6671, "unit": "kPa"}

Answer: 73.6671

Prompt: An ideal gas sample has n=1.72 mol, T=272 K, and V=52.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.72 * 8.314 * 272 / 52.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1125 * 2.03 * 101.
Final: {"answer": 230658.75, "unit": "J"}

Answer: 230658.75

Prompt: A 1125 g sample has specific heat 2.03 J/(g*K). How much heat is needed to raise its temperature by 101 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1125 * 2.03 * 101.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=10.5 V and R=149.9 ohm.
Final: {"answer": 0.7355, "unit": "W"}

Answer: 0.7355

Prompt: A resistor has resistance 149.9 ohm and voltage 10.5 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=10.5 V and R=149.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=442.5 mg, t=198.5 h, and T_half=106 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 120.8348, "unit": "mg"}

Answer: 120.8348

Prompt: A radioactive sample starts with 442.5 mg. Its half-life is 106 hours. How many mg remain after 198.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=442.5 mg, t=198.5 h, and T_half=106 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 900 mL to 0.9 L.
3. Compute M = 4.325 / 0.9.
Final: {"answer": 4.8056, "unit": "mol/L"}

Answer: 4.8056

Prompt: A solution contains 4.325 mol of solute in 900 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 900 mL to 0.9 L.
Compute M = 4.325 / 0.9.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 7.1252, "unit": "state_units"}

Answer: 7.1252

Prompt: Use explicit Euler on dy/dt = -0.11 y with y(0)=12, step size h=1.45, 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) = -0.11 y, so each step multiplies y by 1 - h*0.11.
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(-2)=23.8 and f(0.7)=6.52.
3. The interval width is 2.7.
Final: {"answer": 40.932, "unit": "area_units"}

Answer: 40.932

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.4x+11 from x=-2 to x=0.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-2)=23.8 and f(0.7)=6.52.
The interval width is 2.7.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 49210.0 / 1000.
Final: {"answer": 49.21, "unit": "kg"}

Answer: 49.21

Prompt: Convert 49210 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 49210.0 / 1000.


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

Answer: consistent

Prompt: In field worksheet case 801030, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def clamp_005092(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_005092"}

Answer: python_code

Prompt: Write a Python function clamp_005092(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.

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

try:
    clamp_005092(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 4519 items and budget 65025, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 8.4 kg and a = 4.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 39.9, "unit": "N"}

Answer: 39.9

Prompt: A cart has mass 8.4 kg and measured acceleration 4.75 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 = 8.4 kg and a = 4.75 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 = 41.2^2 and multiply by 0.5 * 27.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 23636.852, "unit": "J"}

Answer: 23636.852

Prompt: A body of mass 27.85 kg moves at 41.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 41.2^2 and multiply by 0.5 * 27.85.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=61 degrees through the sine of 2 theta.
3. Substitute v=25.8 m/s and g=9.81 m/s^2.
Final: {"answer": 57.5428, "unit": "m"}

Answer: 57.5428

Prompt: A projectile is launched on level ground with no air resistance at speed 25.8 m/s and angle 61 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=61 degrees through the sine of 2 theta.
Substitute v=25.8 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 = 2.07 * 8.314 * 270 / 119.0.
Final: {"answer": 39.0479, "unit": "kPa"}

Answer: 39.0479

Prompt: An ideal gas sample has n=2.07 mol, T=270 K, and V=119.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.07 * 8.314 * 270 / 119.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1250 * 0.755 * 116.
Final: {"answer": 109475.0, "unit": "J"}

Answer: 109475.0

Prompt: A 1250 g sample has specific heat 0.755 J/(g*K). How much heat is needed to raise its temperature by 116 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1250 * 0.755 * 116.


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=71.6 V and R=84.4 ohm.
Final: {"answer": 60.7412, "unit": "W"}

Answer: 60.7412

Prompt: A resistor has resistance 84.4 ohm and voltage 71.6 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=71.6 V and R=84.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=622 mg, t=50.5 h, and T_half=1.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0, "unit": "mg"}

Answer: 0.0

Prompt: A radioactive sample starts with 622 mg. Its half-life is 1.5 hours. How many mg remain after 50.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=622 mg, t=50.5 h, and T_half=1.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.13 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 744.0443, "unit": "g"}

Answer: 744.0443

Prompt: A sample contains 4.13 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.13 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.88 y with y(0)=64.5, step size h=0.85, for 11 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.
Apply that update for 11 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(6.4)=-45.66 and f(7.6)=-53.34.
3. The interval width is 1.2.
Final: {"answer": -59.4, "unit": "area_units"}

Answer: -59.4

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.4x+-4.7 from x=6.4 to x=7.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.4)=-45.66 and f(7.6)=-53.34.
The interval width is 1.2.