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

```python
def weighted_sum_005578(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_005578"}

Answer: python_code

Prompt: Write a Python function weighted_sum_005578(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

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

try:
    weighted_sum_005578([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 knapsack scoring problem with 2308 items and budget 10860, 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 = 16.15 kg and a = 12.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 204.2975, "unit": "N"}

Answer: 204.2975

Prompt: A cart has mass 16.15 kg and measured acceleration 12.65 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 = 16.15 kg and a = 12.65 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 = 44.5^2 and multiply by 0.5 * 9.4.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 9307.175, "unit": "J"}

Answer: 9307.175

Prompt: A body of mass 9.4 kg moves at 44.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 44.5^2 and multiply by 0.5 * 9.4.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.45 * 8.314 * 516 / 118.3.
Final: {"answer": 88.8467, "unit": "kPa"}

Answer: 88.8467

Prompt: An ideal gas sample has n=2.45 mol, T=516 K, and V=118.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.45 * 8.314 * 516 / 118.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 870 * 1.765 * 54.
Final: {"answer": 82919.7, "unit": "J"}

Answer: 82919.7

Prompt: A 870 g sample has specific heat 1.765 J/(g*K). How much heat is needed to raise its temperature by 54 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 870 * 1.765 * 54.


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=60.4 V and R=43.5 ohm.
Final: {"answer": 83.8657, "unit": "W"}

Answer: 83.8657

Prompt: A resistor has resistance 43.5 ohm and voltage 60.4 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=60.4 V and R=43.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=814 mg, t=2.5 h, and T_half=51 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 786.8067, "unit": "mg"}

Answer: 786.8067

Prompt: A radioactive sample starts with 814 mg. Its half-life is 51 hours. How many mg remain after 2.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=814 mg, t=2.5 h, and T_half=51 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.42 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 316.7448, "unit": "g"}

Answer: 316.7448

Prompt: A sample contains 5.42 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 = 5.42 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 2725 mL to 2.725 L.
3. Compute M = 0.095 / 2.725.
Final: {"answer": 0.0349, "unit": "mol/L"}

Answer: 0.0349

Prompt: A solution contains 0.095 mol of solute in 2725 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2725 mL to 2.725 L.
Compute M = 0.095 / 2.725.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.36 y, so each step multiplies y by 1 - h*0.36.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 21.5738, "unit": "state_units"}

Answer: 21.5738

Prompt: Use explicit Euler on dy/dt = -0.36 y with y(0)=48, step size h=0.65, for 3 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.36 y, so each step multiplies y by 1 - h*0.36.
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(-7.3)=-20 and f(-0.3)=15.
3. The interval width is 7.
Final: {"answer": -17.5, "unit": "area_units"}

Answer: -17.5

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5x+16.5 from x=-7.3 to x=-0.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.3)=-20 and f(-0.3)=15.
The interval width is 7.

(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=0.34 and add it to the current value.
Final: {"answer": [1.567, 0.838, 0.978], "unit": "temperature_units"}

Answer: 1.567

Answer: 0.838

Answer: 0.978

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=1.7, right=1.85; current interior values are [1.55, 1.45, -0.45]. Use r=0.34. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.34 and add it to the current value.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=121 degrees and keep the unit as newtons.
Final: {"answer": [-173.0528, 288.0082], "unit": "N"}

Answer: -173.0528

Answer: 288.0082

Prompt: A vector has magnitude 336 N at 121 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=121 degrees and keep the unit as newtons.

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


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [1.1, 29.0], "unit": "dimensionless"}

Answer: 1.1

Answer: 29.0

Prompt: A line passes through points (-3, 25.7) and (10.5, 40.55). 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. 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 field worksheet case 87092, 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 finite_differences_005596(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_005596"}

Answer: python_code

Prompt: Write a Python function finite_differences_005596(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.

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

assert finite_differences_005596([5]) == []

assert finite_differences_005596([]) == []


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 83 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 = 4.45 kg and a = 14.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 64.97, "unit": "N"}

Answer: 64.97

Prompt: A cart has mass 4.45 kg and measured acceleration 14.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 4.45 kg and a = 14.6 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 41.15^2 and multiply by 0.5 * 19.5.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 16509.8944, "unit": "J"}

Answer: 16509.8944

Prompt: A body of mass 19.5 kg moves at 41.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 41.15^2 and multiply by 0.5 * 19.5.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=27 degrees through the sine of 2 theta.
3. Substitute v=65.9 m/s and g=9.81 m/s^2.
Final: {"answer": 358.1455, "unit": "m"}

Answer: 358.1455

Prompt: A projectile is launched on level ground with no air resistance at speed 65.9 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=65.9 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 = 1.56 * 8.314 * 435 / 61.7.
Final: {"answer": 91.4405, "unit": "kPa"}

Answer: 91.4405

Prompt: An ideal gas sample has n=1.56 mol, T=435 K, and V=61.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.56 * 8.314 * 435 / 61.7.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=102.4 V and R=99.7 ohm.
Final: {"answer": 105.1731, "unit": "W"}

Answer: 105.1731

Prompt: A resistor has resistance 99.7 ohm and voltage 102.4 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=102.4 V and R=99.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=644.5 mg, t=217 h, and T_half=74.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 85.5849, "unit": "mg"}

Answer: 85.5849

Prompt: A radioactive sample starts with 644.5 mg. Its half-life is 74.5 hours. How many mg remain after 217 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=644.5 mg, t=217 h, and T_half=74.5 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 = 0.72 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 42.0768, "unit": "g"}

Answer: 42.0768

Prompt: A sample contains 0.72 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.72 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 1305 mL to 1.305 L.
3. Compute M = 1.665 / 1.305.
Final: {"answer": 1.2759, "unit": "mol/L"}

Answer: 1.2759

Prompt: A solution contains 1.665 mol of solute in 1305 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1305 mL to 1.305 L.
Compute M = 1.665 / 1.305.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.44 y, so each step multiplies y by 1 - h*0.44.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 6.629, "unit": "state_units"}

Answer: 6.629

Prompt: Use explicit Euler on dy/dt = -0.44 y with y(0)=15.5, step size h=0.3, 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) = -0.44 y, so each step multiplies y by 1 - h*0.44.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-9.4)=6.22 and f(-9.2)=6.36.
3. The interval width is 0.2.
Final: {"answer": 1.258, "unit": "area_units"}

Answer: 1.258

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.7x+12.8 from x=-9.4 to x=-9.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.4)=6.22 and f(-9.2)=6.36.
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=0.46 and add it to the current value.
Final: {"answer": [0.755, 0.421, 0.209], "unit": "temperature_units"}

Answer: 0.755

Answer: 0.421

Answer: 0.209

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=-1.75; current interior values are [-0.05, 2.1, 0.6]. Use r=0.46. 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=0.46 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=69 degrees and keep the unit as newtons.
Final: {"answer": [162.3407, 422.9119], "unit": "N"}

Answer: 162.3407

Answer: 422.9119

Prompt: A vector has magnitude 453 N at 69 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=69 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-9.95, 21.25], "unit": "dimensionless"}

Answer: -9.95

Answer: 21.25

Prompt: A line passes through points (4.25, -21.0375) and (16, -137.95). 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 simulation spec case 392387, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 registry survey record from batch 615205 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 = 4.35 kg and a = 9.35 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 40.6725, "unit": "N"}

Answer: 40.6725

Prompt: A cart has mass 4.35 kg and measured acceleration 9.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 4.35 kg and a = 9.35 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=31 degrees through the sine of 2 theta.
3. Substitute v=11.2 m/s and g=9.81 m/s^2.
Final: {"answer": 11.2902, "unit": "m"}

Answer: 11.2902

Prompt: A projectile is launched on level ground with no air resistance at speed 11.2 m/s and angle 31 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=31 degrees through the sine of 2 theta.
Substitute v=11.2 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=20 mg, t=335.5 h, and T_half=0.5 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 20 mg. Its half-life is 0.5 hours. How many mg remain after 335.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=20 mg, t=335.5 h, and T_half=0.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.83 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 340.7052, "unit": "g"}

Answer: 340.7052

Prompt: A sample contains 5.83 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 = 5.83 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 1795 mL to 1.795 L.
3. Compute M = 3.745 / 1.795.
Final: {"answer": 2.0864, "unit": "mol/L"}

Answer: 2.0864

Prompt: A solution contains 3.745 mol of solute in 1795 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1795 mL to 1.795 L.
Compute M = 3.745 / 1.795.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-9.7)=-61.37 and f(-7.6)=-46.46.
3. The interval width is 2.1.
Final: {"answer": -113.2215, "unit": "area_units"}

Answer: -113.2215

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.1x+7.5 from x=-9.7 to x=-7.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.7)=-61.37 and f(-7.6)=-46.46.
The interval width is 2.1.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.38 and add it to the current value.
Final: {"answer": [-0.827, -0.365, -0.301], "unit": "temperature_units"}

Answer: -0.827

Answer: -0.365

Answer: -0.301

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.45, right=0.65; current interior values are [-0.2, -1.6, 0.25]. Use r=0.38. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=120 degrees and keep the unit as newtons.
Final: {"answer": [-212.25, 367.6278], "unit": "N"}

Answer: -212.25

Answer: 367.6278

Prompt: A vector has magnitude 424.5 N at 120 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=120 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [8.6, -3.25], "unit": "dimensionless"}

Answer: 8.6

Answer: -3.25

Prompt: A line passes through points (-15.5, -136.55) and (-3.5, -33.35). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In quality-control check case 768634, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def threshold_flags_005632(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_005632"}

Answer: python_code

Prompt: Write a Python function threshold_flags_005632(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_005632([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_005632([], 5) == []

assert threshold_flags_005632([-1, 0], 0) == [False, True]


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=4.48 mol and T=280 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 = 1.25 kg and a = 11.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 14.0625, "unit": "N"}

Answer: 14.0625

Prompt: A cart has mass 1.25 kg and measured acceleration 11.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 1.25 kg and a = 11.25 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 = 23.7^2 and multiply by 0.5 * 18.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5139.4635, "unit": "J"}

Answer: 5139.4635

Prompt: A body of mass 18.3 kg moves at 23.7 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 23.7^2 and multiply by 0.5 * 18.3.
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 = 2.62 * 8.314 * 346 / 104.2.
Final: {"answer": 72.3302, "unit": "kPa"}

Answer: 72.3302

Prompt: An ideal gas sample has n=2.62 mol, T=346 K, and V=104.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.62 * 8.314 * 346 / 104.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1960 * 3.83 * 64.
Final: {"answer": 480435.2, "unit": "J"}

Answer: 480435.2

Prompt: A 1960 g sample has specific heat 3.83 J/(g*K). How much heat is needed to raise its temperature by 64 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1960 * 3.83 * 64.


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=54.3 V and R=114.9 ohm.
Final: {"answer": 25.6614, "unit": "W"}

Answer: 25.6614

Prompt: A resistor has resistance 114.9 ohm and voltage 54.3 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=54.3 V and R=114.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=878 mg, t=204 h, and T_half=34.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 14.5711, "unit": "mg"}

Answer: 14.5711

Prompt: A radioactive sample starts with 878 mg. Its half-life is 34.5 hours. How many mg remain after 204 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=878 mg, t=204 h, and T_half=34.5 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 = 6.96 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 306.3096, "unit": "g"}

Answer: 306.3096

Prompt: A sample contains 6.96 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 = 6.96 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 1325 mL to 1.325 L.
3. Compute M = 1.685 / 1.325.
Final: {"answer": 1.2717, "unit": "mol/L"}

Answer: 1.2717

Prompt: A solution contains 1.685 mol of solute in 1325 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1325 mL to 1.325 L.
Compute M = 1.685 / 1.325.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.7 y, so each step multiplies y by 1 - h*0.7.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.7 y with y(0)=15, step size h=1.55, 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) = -0.7 y, so each step multiplies y by 1 - h*0.7.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-7.6)=1.6 and f(-4.1)=-7.15.
3. The interval width is 3.5.
Final: {"answer": -9.7125, "unit": "area_units"}

Answer: -9.7125

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.5x+-17.4 from x=-7.6 to x=-4.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.6)=1.6 and f(-4.1)=-7.15.
The interval width is 3.5.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.34 and add it to the current value.
Final: {"answer": [-1.061, -0.055, -0.766], "unit": "temperature_units"}

Answer: -1.061

Answer: -0.055

Answer: -0.766

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.95, right=-1.6; current interior values are [0.35, -1.5, 0.9]. Use r=0.34. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.34 and add it to the current value.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=124 degrees and keep the unit as newtons.
Final: {"answer": [-20.1309, 29.8454], "unit": "N"}

Answer: -20.1309

Answer: 29.8454

Prompt: A vector has magnitude 36 N at 124 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=124 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": [2.05, -28.5], "unit": "dimensionless"}

Answer: 2.05

Answer: -28.5

Prompt: A line passes through points (3, -22.35) and (5, -18.25). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. 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 model card equation case 755367, 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=0.02 and interior values [-0.9, 2.3, 0.45], 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 = 23.1 kg and a = 3.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 88.935, "unit": "N"}

Answer: 88.935

Prompt: A cart has mass 23.1 kg and measured acceleration 3.85 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 = 23.1 kg and a = 3.85 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=22 degrees through the sine of 2 theta.
3. Substitute v=35.5 m/s and g=9.81 m/s^2.
Final: {"answer": 89.2399, "unit": "m"}

Answer: 89.2399

Prompt: A projectile is launched on level ground with no air resistance at speed 35.5 m/s and angle 22 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=22 degrees through the sine of 2 theta.
Substitute v=35.5 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.94 * 8.314 * 344 / 2.3.
Final: {"answer": 4899.3318, "unit": "kPa"}

Answer: 4899.3318

Prompt: An ideal gas sample has n=3.94 mol, T=344 K, and V=2.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.94 * 8.314 * 344 / 2.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 630 * 0.985 * 118.
Final: {"answer": 73224.9, "unit": "J"}

Answer: 73224.9

Prompt: A 630 g sample has specific heat 0.985 J/(g*K). How much heat is needed to raise its temperature by 118 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 630 * 0.985 * 118.


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=148.7 V and R=97 ohm.
Final: {"answer": 227.9556, "unit": "W"}

Answer: 227.9556

Prompt: A resistor has resistance 97 ohm and voltage 148.7 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=148.7 V and R=97 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.39 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 281.2239, "unit": "g"}

Answer: 281.2239

Prompt: A sample contains 6.39 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 = 6.39 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 4415 mL to 4.415 L.
3. Compute M = 1.8 / 4.415.
Final: {"answer": 0.4077, "unit": "mol/L"}

Answer: 0.4077

Prompt: A solution contains 1.8 mol of solute in 4415 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4415 mL to 4.415 L.
Compute M = 1.8 / 4.415.


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=0.08 and add it to the current value.
Final: {"answer": [-0.32, -1.63, 0.092], "unit": "temperature_units"}

Answer: -0.32

Answer: -1.63

Answer: 0.092

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=0.05, right=-0.05; current interior values are [-0.2, -1.95, 0.3]. Use r=0.08. 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=0.08 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 218.5 + 273.15.
Final: {"answer": 491.65, "unit": "K"}

Answer: 491.65

Prompt: Convert 218.5 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 218.5 + 273.15.


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

```python
def finite_differences_005668(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_005668"}

Answer: python_code

Prompt: Write a Python function finite_differences_005668(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.

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

assert finite_differences_005668([5]) == []

assert finite_differences_005668([]) == []


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=4.54 mol and T=285 K, but does not give volume. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 23.85 kg and a = 8.9 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 212.265, "unit": "N"}

Answer: 212.265

Prompt: A cart has mass 23.85 kg and measured acceleration 8.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 23.85 kg and a = 8.9 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 27.65^2 and multiply by 0.5 * 3.1.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1185.0099, "unit": "J"}

Answer: 1185.0099

Prompt: A body of mass 3.1 kg moves at 27.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 27.65^2 and multiply by 0.5 * 3.1.
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=24 degrees through the sine of 2 theta.
3. Substitute v=8.5 m/s and g=9.81 m/s^2.
Final: {"answer": 5.4732, "unit": "m"}

Answer: 5.4732

Prompt: A projectile is launched on level ground with no air resistance at speed 8.5 m/s and angle 24 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=24 degrees through the sine of 2 theta.
Substitute v=8.5 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.39 * 8.314 * 366 / 40.8.
Final: {"answer": 252.8312, "unit": "kPa"}

Answer: 252.8312

Prompt: An ideal gas sample has n=3.39 mol, T=366 K, and V=40.8 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 = 3.39 * 8.314 * 366 / 40.8.


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=105.6 V and R=179.5 ohm.
Final: {"answer": 62.1246, "unit": "W"}

Answer: 62.1246

Prompt: A resistor has resistance 179.5 ohm and voltage 105.6 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=105.6 V and R=179.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=889 mg, t=100 h, and T_half=41.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 167.3125, "unit": "mg"}

Answer: 167.3125

Prompt: A radioactive sample starts with 889 mg. Its half-life is 41.5 hours. How many mg remain after 100 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=889 mg, t=100 h, and T_half=41.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.74 y, so each step multiplies y by 1 - h*0.74.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": -2.3603, "unit": "state_units"}

Answer: -2.3603

Prompt: Use explicit Euler on dy/dt = -0.74 y with y(0)=64.5, step size h=1.8, for 3 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.74 y, so each step multiplies y by 1 - h*0.74.
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(6.8)=-33.36 and f(16.5)=-108.05.
3. The interval width is 9.7.
Final: {"answer": -685.8385, "unit": "area_units"}

Answer: -685.8385

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.7x+19 from x=6.8 to x=16.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.8)=-33.36 and f(16.5)=-108.05.
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=0.3 and add it to the current value.
Final: {"answer": [0.66, 1.35, 0.475], "unit": "temperature_units"}

Answer: 0.66

Answer: 1.35

Answer: 0.475

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.45, right=-1; current interior values are [1.95, 1.05, 1.15]. 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 2332.0 / 100.
Final: {"answer": 23.32, "unit": "m"}

Answer: 23.32

Prompt: Convert 2332 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 2332.0 / 100.


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

Answer: consistent

Prompt: In quality-control check case 610144, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def running_total_005686(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_005686"}

Answer: python_code

Prompt: Write a Python function running_total_005686(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. Use Newton's second law F = m a.
2. Substitute m = 3.3 kg and a = 15.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 52.305, "unit": "N"}

Answer: 52.305

Prompt: A cart has mass 3.3 kg and measured acceleration 15.85 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 = 3.3 kg and a = 15.85 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 = 13.35^2 and multiply by 0.5 * 26.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2334.7148, "unit": "J"}

Answer: 2334.7148

Prompt: A body of mass 26.2 kg moves at 13.35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 13.35^2 and multiply by 0.5 * 26.2.
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 = 3.04 * 8.314 * 606 / 63.1.
Final: {"answer": 242.7319, "unit": "kPa"}

Answer: 242.7319

Prompt: An ideal gas sample has n=3.04 mol, T=606 K, and V=63.1 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 = 3.04 * 8.314 * 606 / 63.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 395 * 1.32 * 68.
Final: {"answer": 35455.2, "unit": "J"}

Answer: 35455.2

Prompt: A 395 g sample has specific heat 1.32 J/(g*K). How much heat is needed to raise its temperature by 68 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 395 * 1.32 * 68.


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=32 V and R=79.2 ohm.
Final: {"answer": 12.9293, "unit": "W"}

Answer: 12.9293

Prompt: A resistor has resistance 79.2 ohm and voltage 32 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=32 V and R=79.2 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=259.5 mg, t=205.5 h, and T_half=44.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 10.5679, "unit": "mg"}

Answer: 10.5679

Prompt: A radioactive sample starts with 259.5 mg. Its half-life is 44.5 hours. How many mg remain after 205.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=259.5 mg, t=205.5 h, and T_half=44.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.96 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1434.0418, "unit": "g"}

Answer: 1434.0418

Prompt: A sample contains 7.96 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 = 7.96 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 1040 mL to 1.04 L.
3. Compute M = 2.58 / 1.04.
Final: {"answer": 2.4808, "unit": "mol/L"}

Answer: 2.4808

Prompt: A solution contains 2.58 mol of solute in 1040 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1040 mL to 1.04 L.
Compute M = 2.58 / 1.04.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.16 y, so each step multiplies y by 1 - h*0.16.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 35.0403, "unit": "state_units"}

Answer: 35.0403

Prompt: Use explicit Euler on dy/dt = -0.16 y with y(0)=69.5, step size h=0.8, 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) = -0.16 y, so each step multiplies y by 1 - h*0.16.
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)=-8.62 and f(9.6)=5.02.
3. The interval width is 6.2.
Final: {"answer": -11.16, "unit": "area_units"}

Answer: -11.16

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2.2x+-16.1 from x=3.4 to x=9.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3.4)=-8.62 and f(9.6)=5.02.
The interval width is 6.2.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.04 and add it to the current value.
Final: {"answer": [-0.624, 2.088, 0.122], "unit": "temperature_units"}

Answer: -0.624

Answer: 2.088

Answer: 0.122

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=-0.65, right=-0.4; current interior values are [-0.75, 2.3, 0.05]. 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. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=108 degrees and keep the unit as newtons.
Final: {"answer": [-116.1904, 357.5973], "unit": "N"}

Answer: -116.1904

Answer: 357.5973

Prompt: A vector has magnitude 376 N at 108 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=108 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": [-5.9, 8.0], "unit": "dimensionless"}

Answer: -5.9

Answer: 8.0

Prompt: A line passes through points (0, 8) and (9, -45.1). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In model card equation case 242114, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
import math

def unit_vector_005704(x, y):
    norm = math.hypot(x, y)
    if norm == 0:
        raise ValueError('zero vector has no direction')
    return (x / norm, y / norm)
```
Final: {"answer": "python_code", "function": "unit_vector_005704"}

Answer: python_code

Prompt: Write a Python function unit_vector_005704(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.

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

try:
    unit_vector_005704(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 21.65 kg and a = 1.8 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 38.97, "unit": "N"}

Answer: 38.97

Prompt: A cart has mass 21.65 kg and measured acceleration 1.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 21.65 kg and a = 1.8 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 10.65^2 and multiply by 0.5 * 24.1.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1366.7411, "unit": "J"}

Answer: 1366.7411

Prompt: A body of mass 24.1 kg moves at 10.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 10.65^2 and multiply by 0.5 * 24.1.
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=22 degrees through the sine of 2 theta.
3. Substitute v=63.6 m/s and g=9.81 m/s^2.
Final: {"answer": 286.4287, "unit": "m"}

Answer: 286.4287

Prompt: A projectile is launched on level ground with no air resistance at speed 63.6 m/s and angle 22 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=22 degrees through the sine of 2 theta.
Substitute v=63.6 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 = 2.82 * 8.314 * 267 / 17.4.
Final: {"answer": 359.7668, "unit": "kPa"}

Answer: 359.7668

Prompt: An ideal gas sample has n=2.82 mol, T=267 K, and V=17.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.82 * 8.314 * 267 / 17.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 30 * 2.44 * 88.
Final: {"answer": 6441.6, "unit": "J"}

Answer: 6441.6

Prompt: A 30 g sample has specific heat 2.44 J/(g*K). How much heat is needed to raise its temperature by 88 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 30 * 2.44 * 88.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=48.6 V and R=38.7 ohm.
Final: {"answer": 61.0326, "unit": "W"}

Answer: 61.0326

Prompt: A resistor has resistance 38.7 ohm and voltage 48.6 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=48.6 V and R=38.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=926 mg, t=163.5 h, and T_half=101.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 303.18, "unit": "mg"}

Answer: 303.18

Prompt: A radioactive sample starts with 926 mg. Its half-life is 101.5 hours. How many mg remain after 163.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=926 mg, t=163.5 h, and T_half=101.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 1.1235, "unit": "state_units"}

Answer: 1.1235

Prompt: Use explicit Euler on dy/dt = -0.78 y with y(0)=55, step size h=0.45, for 9 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.
Apply that update for 9 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(6.9)=7.76 and f(13.5)=23.6.
3. The interval width is 6.6.
Final: {"answer": 103.488, "unit": "area_units"}

Answer: 103.488

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2.4x+-8.8 from x=6.9 to x=13.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.9)=7.76 and f(13.5)=23.6.
The interval width is 6.6.


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=0.14 and add it to the current value.
Final: {"answer": [0.431, 2.008, 0.679], "unit": "temperature_units"}

Answer: 0.431

Answer: 2.008

Answer: 0.679

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.1, right=0.3; current interior values are [-0.15, 2.75, 0.35]. Use r=0.14. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 35905.0 / 1000.
Final: {"answer": 35.905, "unit": "kg"}

Answer: 35.905

Prompt: Convert 35905 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 35905.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=262 degrees and keep the unit as newtons.
Final: {"answer": [-33.5407, -238.6546], "unit": "N"}

Answer: -33.5407

Answer: -238.6546

Prompt: A vector has magnitude 241 N at 262 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=262 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [7.45, 29.25], "unit": "dimensionless"}

Answer: 7.45

Answer: 29.25

Prompt: A line passes through points (11, 111.2) and (25.75, 221.088). 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 sensor calibration case 318056, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def pairwise_ratios_005722(numerators, denominators):
    if len(numerators) != len(denominators):
        raise ValueError('length mismatch')
    out = []
    for numerator, denominator in zip(numerators, denominators):
        if denominator == 0:
            raise ValueError('zero denominator')
        out.append(numerator / denominator)
    return out
```
Final: {"answer": "python_code", "function": "pairwise_ratios_005722"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_005722(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.

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

try:
    pairwise_ratios_005722([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_005722([1, 2], [1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 registry clinical record from batch 796402 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 = 9.85 kg and a = 1.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 12.3125, "unit": "N"}

Answer: 12.3125

Prompt: A cart has mass 9.85 kg and measured acceleration 1.25 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 = 9.85 kg and a = 1.25 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 = 31.6^2 and multiply by 0.5 * 20.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 10335.096, "unit": "J"}

Answer: 10335.096

Prompt: A body of mass 20.7 kg moves at 31.6 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 31.6^2 and multiply by 0.5 * 20.7.
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=33 degrees through the sine of 2 theta.
3. Substitute v=11.6 m/s and g=9.81 m/s^2.
Final: {"answer": 12.5308, "unit": "m"}

Answer: 12.5308

Prompt: A projectile is launched on level ground with no air resistance at speed 11.6 m/s and angle 33 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=33 degrees through the sine of 2 theta.
Substitute v=11.6 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 = 2.04 * 8.314 * 553 / 9.1.
Final: {"answer": 1030.6802, "unit": "kPa"}

Answer: 1030.6802

Prompt: An ideal gas sample has n=2.04 mol, T=553 K, and V=9.1 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 = 2.04 * 8.314 * 553 / 9.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1390 * 1.555 * 116.
Final: {"answer": 250728.2, "unit": "J"}

Answer: 250728.2

Prompt: A 1390 g sample has specific heat 1.555 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 = 1390 * 1.555 * 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=81 V and R=95 ohm.
Final: {"answer": 69.0632, "unit": "W"}

Answer: 69.0632

Prompt: A resistor has resistance 95 ohm and voltage 81 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=81 V and R=95 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.49 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 249.2166, "unit": "g"}

Answer: 249.2166

Prompt: A sample contains 2.49 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 = 2.49 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 3130 mL to 3.13 L.
3. Compute M = 4.59 / 3.13.
Final: {"answer": 1.4665, "unit": "mol/L"}

Answer: 1.4665

Prompt: A solution contains 4.59 mol of solute in 3130 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3130 mL to 3.13 L.
Compute M = 4.59 / 3.13.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 17.9141, "unit": "state_units"}

Answer: 17.9141

Prompt: Use explicit Euler on dy/dt = -0.12 y with y(0)=58.5, 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) = -0.12 y, so each step multiplies y by 1 - h*0.12.
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(9.4)=-20.98 and f(14.9)=-33.08.
3. The interval width is 5.5.
Final: {"answer": -148.665, "unit": "area_units"}

Answer: -148.665

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.2x+-0.3 from x=9.4 to x=14.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.4)=-20.98 and f(14.9)=-33.08.
The interval width is 5.5.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 679.5 / 100.
Final: {"answer": 6.795, "unit": "m"}

Answer: 6.795

Prompt: Convert 679.5 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 679.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=126 degrees and keep the unit as newtons.
Final: {"answer": [-6.4656, 8.8992], "unit": "N"}

Answer: -6.4656

Answer: 8.8992

Prompt: A vector has magnitude 11 N at 126 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=126 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [6.35, -9.75], "unit": "dimensionless"}

Answer: 6.35

Answer: -9.75

Prompt: A line passes through points (13.75, 77.5625) and (21, 123.6). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In sensor calibration case 787427, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def weighted_sum_005740(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_005740"}

Answer: python_code

Prompt: Write a Python function weighted_sum_005740(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.

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

try:
    weighted_sum_005740([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 20.05 kg and a = 13.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 262.655, "unit": "N"}

Answer: 262.655

Prompt: A cart has mass 20.05 kg and measured acceleration 13.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 20.05 kg and a = 13.1 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=29 degrees through the sine of 2 theta.
3. Substitute v=81.5 m/s and g=9.81 m/s^2.
Final: {"answer": 574.2046, "unit": "m"}

Answer: 574.2046

Prompt: A projectile is launched on level ground with no air resistance at speed 81.5 m/s and angle 29 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=29 degrees through the sine of 2 theta.
Substitute v=81.5 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.6 * 8.314 * 425 / 96.4.
Final: {"answer": 58.6465, "unit": "kPa"}

Answer: 58.6465

Prompt: An ideal gas sample has n=1.6 mol, T=425 K, and V=96.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.6 * 8.314 * 425 / 96.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 555 * 1.33 * 66.
Final: {"answer": 48717.9, "unit": "J"}

Answer: 48717.9

Prompt: A 555 g sample has specific heat 1.33 J/(g*K). How much heat is needed to raise its temperature by 66 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 555 * 1.33 * 66.


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=46 V and R=114.9 ohm.
Final: {"answer": 18.416, "unit": "W"}

Answer: 18.416

Prompt: A resistor has resistance 114.9 ohm and voltage 46 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=46 V and R=114.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=934 mg, t=115.5 h, and T_half=19 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 13.8166, "unit": "mg"}

Answer: 13.8166

Prompt: A radioactive sample starts with 934 mg. Its half-life is 19 hours. How many mg remain after 115.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=934 mg, t=115.5 h, and T_half=19 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.37 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 324.3537, "unit": "g"}

Answer: 324.3537

Prompt: A sample contains 7.37 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.37 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) = -0.23 y, so each step multiplies y by 1 - h*0.23.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 22.1638, "unit": "state_units"}

Answer: 22.1638

Prompt: Use explicit Euler on dy/dt = -0.23 y with y(0)=39, step size h=0.2, for 12 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.23 y, so each step multiplies y by 1 - h*0.23.
Apply that update for 12 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-8)=75 and f(0.1)=17.49.
3. The interval width is 8.1.
Final: {"answer": 374.5845, "unit": "area_units"}

Answer: 374.5845

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.1x+18.2 from x=-8 to x=0.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-8)=75 and f(0.1)=17.49.
The interval width is 8.1.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=245 degrees and keep the unit as newtons.
Final: {"answer": [-149.1842, -319.9266], "unit": "N"}

Answer: -149.1842

Answer: -319.9266

Prompt: A vector has magnitude 353 N at 245 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=245 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-7.8, -7.5], "unit": "dimensionless"}

Answer: -7.8

Answer: -7.5

Prompt: A line passes through points (-16.5, 121.2) and (-6.25, 41.25). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In simulation spec case 326907, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def clamp_005758(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_005758"}

Answer: python_code

Prompt: Write a Python function clamp_005758(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_005758(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: left_boundary, right_boundary.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.12 and interior values [-0.25, -1.9, 2.85], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 22.2 kg and a = 11.35 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 251.97, "unit": "N"}

Answer: 251.97

Prompt: A cart has mass 22.2 kg and measured acceleration 11.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 22.2 kg and a = 11.35 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=46 degrees through the sine of 2 theta.
3. Substitute v=10.7 m/s and g=9.81 m/s^2.
Final: {"answer": 11.6636, "unit": "m"}

Answer: 11.6636

Prompt: A projectile is launched on level ground with no air resistance at speed 10.7 m/s and angle 46 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=46 degrees through the sine of 2 theta.
Substitute v=10.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.25 * 8.314 * 568 / 116.3.
Final: {"answer": 131.966, "unit": "kPa"}

Answer: 131.966

Prompt: An ideal gas sample has n=3.25 mol, T=568 K, and V=116.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.25 * 8.314 * 568 / 116.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1500 * 2.8 * 61.
Final: {"answer": 256200.0, "unit": "J"}

Answer: 256200.0

Prompt: A 1500 g sample has specific heat 2.8 J/(g*K). How much heat is needed to raise its temperature by 61 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1500 * 2.8 * 61.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=362 mg, t=120 h, and T_half=5.5 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 362 mg. Its half-life is 5.5 hours. How many mg remain after 120 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=362 mg, t=120 h, and T_half=5.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.77 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 577.502, "unit": "g"}

Answer: 577.502

Prompt: A sample contains 5.77 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 = 5.77 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(1.5)=2.85 and f(1.7)=1.43.
3. The interval width is 0.2.
Final: {"answer": 0.428, "unit": "area_units"}

Answer: 0.428

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.1x+13.5 from x=1.5 to x=1.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.5)=2.85 and f(1.7)=1.43.
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=0.26 and add it to the current value.
Final: {"answer": [1.165, 1.19, 0.783], "unit": "temperature_units"}

Answer: 1.165

Answer: 1.19

Answer: 0.783

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.75, right=-0.75; current interior values are [-0.2, 2.1, 0.9]. Use r=0.26. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 9837.0 / 1000.
Final: {"answer": 9.837, "unit": "kg"}

Answer: 9.837

Prompt: Convert 9837 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 9837.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=309 degrees and keep the unit as newtons.
Final: {"answer": [142.5411, -176.0236], "unit": "N"}

Answer: 142.5411

Answer: -176.0236

Prompt: A vector has magnitude 226.5 N at 309 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=309 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [2.7, -15.25], "unit": "dimensionless"}

Answer: 2.7

Answer: -15.25

Prompt: A line passes through points (-6.75, -33.475) and (-3.25, -24.025). 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. volt squared divided by ohm is watt
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In model card equation case 514464, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.48 and interior values [-0.1, 1.1, 2.9], 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 = 24.9 kg and a = 11.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 297.555, "unit": "N"}

Answer: 297.555

Prompt: A cart has mass 24.9 kg and measured acceleration 11.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 24.9 kg and a = 11.95 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 1.2^2 and multiply by 0.5 * 22.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 16.38, "unit": "J"}

Answer: 16.38

Prompt: A body of mass 22.75 kg moves at 1.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 1.2^2 and multiply by 0.5 * 22.75.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=6 degrees through the sine of 2 theta.
3. Substitute v=62.8 m/s and g=9.81 m/s^2.
Final: {"answer": 83.5852, "unit": "m"}

Answer: 83.5852

Prompt: A projectile is launched on level ground with no air resistance at speed 62.8 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=62.8 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 = 1475 * 1.675 * 117.
Final: {"answer": 289063.125, "unit": "J"}

Answer: 289063.125

Prompt: A 1475 g sample has specific heat 1.675 J/(g*K). How much heat is needed to raise its temperature by 117 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1475 * 1.675 * 117.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=1 mg, t=244 h, and T_half=56 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0488, "unit": "mg"}

Answer: 0.0488

Prompt: A radioactive sample starts with 1 mg. Its half-life is 56 hours. How many mg remain after 244 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=1 mg, t=244 h, and T_half=56 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 = 4.93 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 288.1092, "unit": "g"}

Answer: 288.1092

Prompt: A sample contains 4.93 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 = 4.93 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 2620 mL to 2.62 L.
3. Compute M = 0.6 / 2.62.
Final: {"answer": 0.229, "unit": "mol/L"}

Answer: 0.229

Prompt: A solution contains 0.6 mol of solute in 2620 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2620 mL to 2.62 L.
Compute M = 0.6 / 2.62.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.93 y, so each step multiplies y by 1 - h*0.93.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": -20.5862, "unit": "state_units"}

Answer: -20.5862

Prompt: Use explicit Euler on dy/dt = -0.93 y with y(0)=80, step size h=2, for 9 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.93 y, so each step multiplies y by 1 - h*0.93.
Apply that update for 9 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.34 and add it to the current value.
Final: {"answer": [-0.825, -0.114, -0.804], "unit": "temperature_units"}

Answer: -0.825

Answer: -0.114

Answer: -0.804

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 [0.45, -1.1, 0.25]. Use r=0.34. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.34 and add it to the current value.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=306 degrees and keep the unit as newtons.
Final: {"answer": [147.2402, -202.6588], "unit": "N"}

Answer: 147.2402

Answer: -202.6588

Prompt: A vector has magnitude 250.5 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": [8.35, 1.0], "unit": "dimensionless"}

Answer: 8.35

Answer: 1.0

Prompt: A line passes through points (-8.5, -69.975) and (3.75, 32.3125). 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 instrument manual case 223814, 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. 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 946 items and budget 29985, 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 = 16.55 kg and a = 10.35 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 171.2925, "unit": "N"}

Answer: 171.2925

Prompt: A cart has mass 16.55 kg and measured acceleration 10.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 16.55 kg and a = 10.35 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 = 43.7^2 and multiply by 0.5 * 18.45.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 17616.8903, "unit": "J"}

Answer: 17616.8903

Prompt: A body of mass 18.45 kg moves at 43.7 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 43.7^2 and multiply by 0.5 * 18.45.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=65 degrees through the sine of 2 theta.
3. Substitute v=48.3 m/s and g=9.81 m/s^2.
Final: {"answer": 182.171, "unit": "m"}

Answer: 182.171

Prompt: A projectile is launched on level ground with no air resistance at speed 48.3 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=48.3 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 = 0.68 * 8.314 * 322 / 61.3.
Final: {"answer": 29.6971, "unit": "kPa"}

Answer: 29.6971

Prompt: An ideal gas sample has n=0.68 mol, T=322 K, and V=61.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.68 * 8.314 * 322 / 61.3.


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=184.1 V and R=144 ohm.
Final: {"answer": 235.3667, "unit": "W"}

Answer: 235.3667

Prompt: A resistor has resistance 144 ohm and voltage 184.1 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=184.1 V and R=144 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=239.5 mg, t=256 h, and T_half=53 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 8.4193, "unit": "mg"}

Answer: 8.4193

Prompt: A radioactive sample starts with 239.5 mg. Its half-life is 53 hours. How many mg remain after 256 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=239.5 mg, t=256 h, and T_half=53 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.6 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 360.3132, "unit": "g"}

Answer: 360.3132

Prompt: A sample contains 3.6 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 3.6 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 2235 mL to 2.235 L.
3. Compute M = 4.145 / 2.235.
Final: {"answer": 1.8546, "unit": "mol/L"}

Answer: 1.8546

Prompt: A solution contains 4.145 mol of solute in 2235 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2235 mL to 2.235 L.
Compute M = 4.145 / 2.235.