Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 17.5 kg and a = 8.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 144.375, "unit": "N"}

Answer: 144.375

Prompt: A cart has mass 17.5 kg and measured acceleration 8.25 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 = 17.5 kg and a = 8.25 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 13.25^2 and multiply by 0.5 * 9.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 794.4203, "unit": "J"}

Answer: 794.4203

Prompt: A body of mass 9.05 kg moves at 13.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 13.25^2 and multiply by 0.5 * 9.05.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=41 degrees through the sine of 2 theta.
3. Substitute v=55 m/s and g=9.81 m/s^2.
Final: {"answer": 305.3579, "unit": "m"}

Answer: 305.3579

Prompt: A projectile is launched on level ground with no air resistance at speed 55 m/s and angle 41 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=41 degrees through the sine of 2 theta.
Substitute v=55 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 = 2.14 * 8.314 * 253 / 26.4.
Final: {"answer": 170.5063, "unit": "kPa"}

Answer: 170.5063

Prompt: An ideal gas sample has n=2.14 mol, T=253 K, and V=26.4 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 = 2.14 * 8.314 * 253 / 26.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1960 * 2.45 * 111.
Final: {"answer": 533022.0, "unit": "J"}

Answer: 533022.0

Prompt: A 1960 g sample has specific heat 2.45 J/(g*K). How much heat is needed to raise its temperature by 111 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1960 * 2.45 * 111.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=86.2 V and R=31.8 ohm.
Final: {"answer": 233.6616, "unit": "W"}

Answer: 233.6616

Prompt: A resistor has resistance 31.8 ohm and voltage 86.2 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=86.2 V and R=31.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=185 mg, t=293 h, and T_half=53 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 4.0085, "unit": "mg"}

Answer: 4.0085

Prompt: A radioactive sample starts with 185 mg. Its half-life is 53 hours. How many mg remain after 293 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=185 mg, t=293 h, and T_half=53 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.4 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 240.2088, "unit": "g"}

Answer: 240.2088

Prompt: A sample contains 2.4 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 2.4 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 3645 mL to 3.645 L.
3. Compute M = 3.545 / 3.645.
Final: {"answer": 0.9726, "unit": "mol/L"}

Answer: 0.9726

Prompt: A solution contains 3.545 mol of solute in 3645 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3645 mL to 3.645 L.
Compute M = 3.545 / 3.645.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 0.0125, "unit": "state_units"}

Answer: 0.0125

Prompt: Use explicit Euler on dy/dt = -0.71 y with y(0)=5.5, step size h=0.75, for 8 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.
Apply that update for 8 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(3.7)=13.91 and f(11)=38.
3. The interval width is 7.3.
Final: {"answer": 189.4715, "unit": "area_units"}

Answer: 189.4715

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.3x+1.7 from x=3.7 to x=11. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3.7)=13.91 and f(11)=38.
The interval width is 7.3.

(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=0.24 and add it to the current value.
Final: {"answer": [0.942, 0.922, 0.102], "unit": "temperature_units"}

Answer: 0.942

Answer: 0.922

Answer: 0.102

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.9, right=0.65; current interior values are [0.45, 2.05, -1.05]. Use r=0.24. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 46.0 + 273.15.
Final: {"answer": 319.15, "unit": "K"}

Answer: 319.15

Prompt: Convert 46 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 46.0 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=226 degrees and keep the unit as newtons.
Final: {"answer": [-56.962, -58.9859], "unit": "N"}

Answer: -56.962

Answer: -58.9859

Prompt: A vector has magnitude 82 N at 226 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=226 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": [-8.8, 7.75], "unit": "dimensionless"}

Answer: -8.8

Answer: 7.75

Prompt: A line passes through points (-7.25, 71.55) and (6.75, -51.65). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In sensor calibration case 440140, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def finite_differences_006496(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_006496"}

Answer: python_code

Prompt: Write a Python function finite_differences_006496(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_006496([5]) == []

assert finite_differences_006496([]) == []


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 9.35 kg and a = 0.8 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 7.48, "unit": "N"}

Answer: 7.48

Prompt: A cart has mass 9.35 kg and measured acceleration 0.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 9.35 kg and a = 0.8 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 6.7^2 and multiply by 0.5 * 26.4.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 592.548, "unit": "J"}

Answer: 592.548

Prompt: A body of mass 26.4 kg moves at 6.7 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 6.7^2 and multiply by 0.5 * 26.4.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=38 degrees through the sine of 2 theta.
3. Substitute v=33.8 m/s and g=9.81 m/s^2.
Final: {"answer": 112.9974, "unit": "m"}

Answer: 112.9974

Prompt: A projectile is launched on level ground with no air resistance at speed 33.8 m/s and angle 38 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=38 degrees through the sine of 2 theta.
Substitute v=33.8 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 = 155 * 3.71 * 27.
Final: {"answer": 15526.35, "unit": "J"}

Answer: 15526.35

Prompt: A 155 g sample has specific heat 3.71 J/(g*K). How much heat is needed to raise its temperature by 27 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 155 * 3.71 * 27.


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=3.3 V and R=58 ohm.
Final: {"answer": 0.1878, "unit": "W"}

Answer: 0.1878

Prompt: A resistor has resistance 58 ohm and voltage 3.3 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=3.3 V and R=58 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.02 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 234.9288, "unit": "g"}

Answer: 234.9288

Prompt: A sample contains 4.02 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 = 4.02 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 1590 mL to 1.59 L.
3. Compute M = 1.74 / 1.59.
Final: {"answer": 1.0943, "unit": "mol/L"}

Answer: 1.0943

Prompt: A solution contains 1.74 mol of solute in 1590 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1590 mL to 1.59 L.
Compute M = 1.74 / 1.59.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 0.6092, "unit": "state_units"}

Answer: 0.6092

Prompt: Use explicit Euler on dy/dt = -0.21 y with y(0)=3, step size h=1.3, 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) = -0.21 y, so each step multiplies y by 1 - h*0.21.
Apply that update for 5 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=0.14 and add it to the current value.
Final: {"answer": [0.982, 0.404, 1.55], "unit": "temperature_units"}

Answer: 0.982

Answer: 0.404

Answer: 1.55

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.2, right=-0.4; current interior values are [1.15, -0.1, 2.25]. 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 28.5 + 273.15.
Final: {"answer": 301.65, "unit": "K"}

Answer: 301.65

Prompt: Convert 28.5 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 28.5 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=214 degrees and keep the unit as newtons.
Final: {"answer": [-371.8234, -250.798], "unit": "N"}

Answer: -371.8234

Answer: -250.798

Prompt: A vector has magnitude 448.5 N at 214 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=214 degrees and keep the unit as newtons.


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 student derivation case 342687, 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 weighted_sum_006514(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_006514"}

Answer: python_code

Prompt: Write a Python function weighted_sum_006514(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_006514([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: 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 ledger record from batch 149509 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 = 18.55 kg and a = 12.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 228.165, "unit": "N"}

Answer: 228.165

Prompt: A cart has mass 18.55 kg and measured acceleration 12.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 18.55 kg and a = 12.3 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 18.4^2 and multiply by 0.5 * 4.1.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 694.048, "unit": "J"}

Answer: 694.048

Prompt: A body of mass 4.1 kg moves at 18.4 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 18.4^2 and multiply by 0.5 * 4.1.
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 = 3.31 * 8.314 * 318 / 64.9.
Final: {"answer": 134.8405, "unit": "kPa"}

Answer: 134.8405

Prompt: An ideal gas sample has n=3.31 mol, T=318 K, and V=64.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.31 * 8.314 * 318 / 64.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1465 * 2.085 * 43.
Final: {"answer": 131344.575, "unit": "J"}

Answer: 131344.575

Prompt: A 1465 g sample has specific heat 2.085 J/(g*K). How much heat is needed to raise its temperature by 43 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1465 * 2.085 * 43.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1685 mL to 1.685 L.
3. Compute M = 2.44 / 1.685.
Final: {"answer": 1.4481, "unit": "mol/L"}

Answer: 1.4481

Prompt: A solution contains 2.44 mol of solute in 1685 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1685 mL to 1.685 L.
Compute M = 2.44 / 1.685.


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=0.48 and add it to the current value.
Final: {"answer": [0.156, 0.73, -0.958], "unit": "temperature_units"}

Answer: 0.156

Answer: 0.73

Answer: -0.958

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.7, right=-1.8; current interior values are [-0.3, -0.35, 1.85]. Use r=0.48. 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=0.48 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 4816.5 / 100.
Final: {"answer": 48.165, "unit": "m"}

Answer: 48.165

Prompt: Convert 4816.5 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 4816.5 / 100.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [6.85, 13.25], "unit": "dimensionless"}

Answer: 6.85

Answer: 13.25

Prompt: A line passes through points (8.75, 73.1875) and (23.5, 174.225). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In simulation spec case 113903, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def center_values_006532(values):
    if not values:
        raise ValueError('center_values requires at least one value')
    mean = sum(values) / len(values)
    return [value - mean for value in values]
```
Final: {"answer": "python_code", "function": "center_values_006532"}

Answer: python_code

Prompt: Write a Python function center_values_006532(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. 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:
    center_values_006532([])
    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 routing scoring problem with 2450 items and budget 61715, 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 = 16.25 kg and a = 0.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 4.0625, "unit": "N"}

Answer: 4.0625

Prompt: A cart has mass 16.25 kg and measured acceleration 0.25 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 = 16.25 kg and a = 0.25 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 = 0.7^2 and multiply by 0.5 * 20.4.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 4.998, "unit": "J"}

Answer: 4.998

Prompt: A body of mass 20.4 kg moves at 0.7 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 0.7^2 and multiply by 0.5 * 20.4.
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 = 1.18 * 8.314 * 332 / 26.8.
Final: {"answer": 121.5333, "unit": "kPa"}

Answer: 121.5333

Prompt: An ideal gas sample has n=1.18 mol, T=332 K, and V=26.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.18 * 8.314 * 332 / 26.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 635 * 3.505 * 20.
Final: {"answer": 44513.5, "unit": "J"}

Answer: 44513.5

Prompt: A 635 g sample has specific heat 3.505 J/(g*K). How much heat is needed to raise its temperature by 20 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 635 * 3.505 * 20.


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=123.4 V and R=20.4 ohm.
Final: {"answer": 746.449, "unit": "W"}

Answer: 746.449

Prompt: A resistor has resistance 20.4 ohm and voltage 123.4 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=123.4 V and R=20.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=358 mg, t=224 h, and T_half=30 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 2.0239, "unit": "mg"}

Answer: 2.0239

Prompt: A radioactive sample starts with 358 mg. Its half-life is 30 hours. How many mg remain after 224 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=358 mg, t=224 h, and T_half=30 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 = 6.99 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 125.9249, "unit": "g"}

Answer: 125.9249

Prompt: A sample contains 6.99 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.99 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3225 mL to 3.225 L.
3. Compute M = 4.675 / 3.225.
Final: {"answer": 1.4496, "unit": "mol/L"}

Answer: 1.4496

Prompt: A solution contains 4.675 mol of solute in 3225 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3225 mL to 3.225 L.
Compute M = 4.675 / 3.225.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.77 y, so each step multiplies y by 1 - h*0.77.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0002, "unit": "state_units"}

Answer: 0.0002

Prompt: Use explicit Euler on dy/dt = -0.77 y with y(0)=26.5, step size h=0.9, 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) = -0.77 y, so each step multiplies y by 1 - h*0.77.
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(0.3)=-14.27 and f(5.6)=-19.04.
3. The interval width is 5.3.
Final: {"answer": -88.2715, "unit": "area_units"}

Answer: -88.2715

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.9x+-14 from x=0.3 to x=5.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(0.3)=-14.27 and f(5.6)=-19.04.
The interval width is 5.3.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.48 and add it to the current value.
Final: {"answer": [1.048, 0.52, 1.87], "unit": "temperature_units"}

Answer: 1.048

Answer: 0.52

Answer: 1.87

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.75, right=2.05; current interior values are [-2.0, 1.6, 2.95]. Use r=0.48. 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=0.48 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 800.0 / 100.
Final: {"answer": 8.0, "unit": "m"}

Answer: 8.0

Prompt: Convert 800 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 800.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=40 degrees and keep the unit as newtons.
Final: {"answer": [158.9542, 133.3784], "unit": "N"}

Answer: 158.9542

Answer: 133.3784

Prompt: A vector has magnitude 207.5 N at 40 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=40 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": [-2.85, -13.5], "unit": "dimensionless"}

Answer: -2.85

Answer: -13.5

Prompt: A line passes through points (4, -24.9) and (8, -36.3). Return [slope, intercept] for y = slope*x + intercept.

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


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

```python
def normalize_006550(values):
    total = sum(values)
    if total == 0:
        raise ValueError('cannot normalize zero-sum values')
    return [v / total for v in values]
```
Final: {"answer": "python_code", "function": "normalize_006550"}

Answer: python_code

Prompt: Write a Python function normalize_006550(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.

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

out = normalize_006550([2, 3, 5]); assert len(out) == 3

try:
    normalize_006550([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=13 and h=0.6, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 12.35^2 and multiply by 0.5 * 29.1.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2219.2024, "unit": "J"}

Answer: 2219.2024

Prompt: A body of mass 29.1 kg moves at 12.35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 12.35^2 and multiply by 0.5 * 29.1.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.85 * 8.314 * 439 / 75.1.
Final: {"answer": 235.7091, "unit": "kPa"}

Answer: 235.7091

Prompt: An ideal gas sample has n=4.85 mol, T=439 K, and V=75.1 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 = 4.85 * 8.314 * 439 / 75.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 235 * 2.235 * 87.
Final: {"answer": 45694.575, "unit": "J"}

Answer: 45694.575

Prompt: A 235 g sample has specific heat 2.235 J/(g*K). How much heat is needed to raise its temperature by 87 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 235 * 2.235 * 87.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=96.7 V and R=189.9 ohm.
Final: {"answer": 49.2411, "unit": "W"}

Answer: 49.2411

Prompt: A resistor has resistance 189.9 ohm and voltage 96.7 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=96.7 V and R=189.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=200 mg, t=244.5 h, and T_half=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 200 mg. Its half-life is 5 hours. How many mg remain after 244.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=200 mg, t=244.5 h, and T_half=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 = 7.15 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 715.6221, "unit": "g"}

Answer: 715.6221

Prompt: A sample contains 7.15 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 = 7.15 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 370 mL to 0.37 L.
3. Compute M = 2.73 / 0.37.
Final: {"answer": 7.3784, "unit": "mol/L"}

Answer: 7.3784

Prompt: A solution contains 2.73 mol of solute in 370 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 370 mL to 0.37 L.
Compute M = 2.73 / 0.37.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(5.9)=-61.43 and f(10.1)=-93.77.
3. The interval width is 4.2.
Final: {"answer": -325.92, "unit": "area_units"}

Answer: -325.92

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.7x+-16 from x=5.9 to x=10.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(5.9)=-61.43 and f(10.1)=-93.77.
The interval width is 4.2.


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=0.06 and add it to the current value.
Final: {"answer": [0.416, -1.624, 0.186], "unit": "temperature_units"}

Answer: 0.416

Answer: -1.624

Answer: 0.186

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.7, right=2.8; current interior values are [0.65, -1.9, 0.15]. Use r=0.06. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4468.5 / 100.
Final: {"answer": 44.685, "unit": "m"}

Answer: 44.685

Prompt: Convert 4468.5 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 4468.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=31 degrees and keep the unit as newtons.
Final: {"answer": [33.4295, 20.0865], "unit": "N"}

Answer: 33.4295

Answer: 20.0865

Prompt: A vector has magnitude 39 N at 31 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=31 degrees and keep the unit as newtons.


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

Answer: consistent

Prompt: In instrument manual case 777541, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def running_total_006568(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_006568"}

Answer: python_code

Prompt: Write a Python function running_total_006568(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

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


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

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a allocation scoring problem with 2203 items and budget 99015, 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 = 9.55 kg and a = 7.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 75.9225, "unit": "N"}

Answer: 75.9225

Prompt: A cart has mass 9.55 kg and measured acceleration 7.95 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 = 9.55 kg and a = 7.95 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 = 10.95^2 and multiply by 0.5 * 13.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 821.3321, "unit": "J"}

Answer: 821.3321

Prompt: A body of mass 13.7 kg moves at 10.95 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 10.95^2 and multiply by 0.5 * 13.7.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.33 * 8.314 * 277 / 60.8.
Final: {"answer": 201.8894, "unit": "kPa"}

Answer: 201.8894

Prompt: An ideal gas sample has n=5.33 mol, T=277 K, and V=60.8 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 = 5.33 * 8.314 * 277 / 60.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 275 * 2.955 * 84.
Final: {"answer": 68260.5, "unit": "J"}

Answer: 68260.5

Prompt: A 275 g sample has specific heat 2.955 J/(g*K). How much heat is needed to raise its temperature by 84 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 275 * 2.955 * 84.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=741.5 mg, t=173.5 h, and T_half=59 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 96.5781, "unit": "mg"}

Answer: 96.5781

Prompt: A radioactive sample starts with 741.5 mg. Its half-life is 59 hours. How many mg remain after 173.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=741.5 mg, t=173.5 h, and T_half=59 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.81 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 32.6072, "unit": "g"}

Answer: 32.6072

Prompt: A sample contains 1.81 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.81 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3450 mL to 3.45 L.
3. Compute M = 3.78 / 3.45.
Final: {"answer": 1.0957, "unit": "mol/L"}

Answer: 1.0957

Prompt: A solution contains 3.78 mol of solute in 3450 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3450 mL to 3.45 L.
Compute M = 3.78 / 3.45.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.29 y, so each step multiplies y by 1 - h*0.29.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 11.5875, "unit": "state_units"}

Answer: 11.5875

Prompt: Use explicit Euler on dy/dt = -0.29 y with y(0)=50, step size h=0.65, for 7 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.29 y, so each step multiplies y by 1 - h*0.29.
Apply that update for 7 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(1.5)=15.5 and f(7)=43.
3. The interval width is 5.5.
Final: {"answer": 160.875, "unit": "area_units"}

Answer: 160.875

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5x+8 from x=1.5 to x=7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.5)=15.5 and f(7)=43.
The interval width is 5.5.


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=0.44 and add it to the current value.
Final: {"answer": [0.614, -0.094, -1.02], "unit": "temperature_units"}

Answer: 0.614

Answer: -0.094

Answer: -1.02

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.15, right=-0.8; current interior values are [1.45, -1.15, -1.35]. Use r=0.44. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.44 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 11568.0 / 1000.
Final: {"answer": 11.568, "unit": "kg"}

Answer: 11.568

Prompt: Convert 11568 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 11568.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=228 degrees and keep the unit as newtons.
Final: {"answer": [-212.7835, -236.3201], "unit": "N"}

Answer: -212.7835

Answer: -236.3201

Prompt: A vector has magnitude 318 N at 228 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=228 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-9.45, -10.0], "unit": "dimensionless"}

Answer: -9.45

Answer: -10.0

Prompt: A line passes through points (9, -95.05) and (21.5, -213.175). Return [slope, intercept] for y = slope*x + intercept.

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


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

```python
def pairwise_ratios_006586(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_006586"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_006586(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_006586([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_006586([1, 2], [1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 18.8 kg and a = 8.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 155.1, "unit": "N"}

Answer: 155.1

Prompt: A cart has mass 18.8 kg and measured acceleration 8.25 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 = 18.8 kg and a = 8.25 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=42 degrees through the sine of 2 theta.
3. Substitute v=23.1 m/s and g=9.81 m/s^2.
Final: {"answer": 54.0965, "unit": "m"}

Answer: 54.0965

Prompt: A projectile is launched on level ground with no air resistance at speed 23.1 m/s and angle 42 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=42 degrees through the sine of 2 theta.
Substitute v=23.1 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 = 750 * 2.04 * 99.
Final: {"answer": 151470.0, "unit": "J"}

Answer: 151470.0

Prompt: A 750 g sample has specific heat 2.04 J/(g*K). How much heat is needed to raise its temperature by 99 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 750 * 2.04 * 99.


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=202.4 V and R=54.5 ohm.
Final: {"answer": 751.6653, "unit": "W"}

Answer: 751.6653

Prompt: A resistor has resistance 54.5 ohm and voltage 202.4 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=202.4 V and R=54.5 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 5.09 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 91.6963, "unit": "g"}

Answer: 91.6963

Prompt: A sample contains 5.09 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 5.09 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(2.8)=24.34 and f(7.2)=56.46.
3. The interval width is 4.4.
Final: {"answer": 177.76, "unit": "area_units"}

Answer: 177.76

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.3x+3.9 from x=2.8 to x=7.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(2.8)=24.34 and f(7.2)=56.46.
The interval width is 4.4.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.28 and add it to the current value.
Final: {"answer": [0.592, 0.956, 1.826], "unit": "temperature_units"}

Answer: 0.592

Answer: 0.956

Answer: 1.826

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=2.65; current interior values are [-1.2, 2.3, 1.0]. Use r=0.28. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.28 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3702.5 / 100.
Final: {"answer": 37.025, "unit": "m"}

Answer: 37.025

Prompt: Convert 3702.5 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 3702.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=303 degrees and keep the unit as newtons.
Final: {"answer": [21.5132, -33.1275], "unit": "N"}

Answer: 21.5132

Answer: -33.1275

Prompt: A vector has magnitude 39.5 N at 303 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=303 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": [5.75, -14.75], "unit": "dimensionless"}

Answer: 5.75

Answer: -14.75

Prompt: A line passes through points (-1.75, -24.8125) and (4.75, 12.5625). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. 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_006604(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_006604"}

Answer: python_code

Prompt: Write a Python function clamp_006604(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_006604(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each laboratory sensor record from batch 13602 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 = 6.7 kg and a = 12.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 82.075, "unit": "N"}

Answer: 82.075

Prompt: A cart has mass 6.7 kg and measured acceleration 12.25 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 = 6.7 kg and a = 12.25 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 = 20.15^2 and multiply by 0.5 * 10.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2192.5215, "unit": "J"}

Answer: 2192.5215

Prompt: A body of mass 10.8 kg moves at 20.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 20.15^2 and multiply by 0.5 * 10.8.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=85 degrees through the sine of 2 theta.
3. Substitute v=71 m/s and g=9.81 m/s^2.
Final: {"answer": 89.2314, "unit": "m"}

Answer: 89.2314

Prompt: A projectile is launched on level ground with no air resistance at speed 71 m/s and angle 85 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=85 degrees through the sine of 2 theta.
Substitute v=71 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 = 1.79 * 8.314 * 559 / 67.5.
Final: {"answer": 123.2455, "unit": "kPa"}

Answer: 123.2455

Prompt: An ideal gas sample has n=1.79 mol, T=559 K, and V=67.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.79 * 8.314 * 559 / 67.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 505 * 2.82 * 37.
Final: {"answer": 52691.7, "unit": "J"}

Answer: 52691.7

Prompt: A 505 g sample has specific heat 2.82 J/(g*K). How much heat is needed to raise its temperature by 37 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 505 * 2.82 * 37.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.72 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 163.7172, "unit": "g"}

Answer: 163.7172

Prompt: A sample contains 3.72 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 = 3.72 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 4165 mL to 4.165 L.
3. Compute M = 2.35 / 4.165.
Final: {"answer": 0.5642, "unit": "mol/L"}

Answer: 0.5642

Prompt: A solution contains 2.35 mol of solute in 4165 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4165 mL to 4.165 L.
Compute M = 2.35 / 4.165.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 0.004, "unit": "state_units"}

Answer: 0.004

Prompt: Use explicit Euler on dy/dt = -0.51 y with y(0)=25.5, step size h=1.4, for 7 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.
Apply that update for 7 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=0.02 and add it to the current value.
Final: {"answer": [-1.389, 2.154, 1.254], "unit": "temperature_units"}

Answer: -1.389

Answer: 2.154

Answer: 1.254

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.7, right=0.45; current interior values are [-1.55, 2.25, 1.25]. Use r=0.02. 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=0.02 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 134.5 + 273.15.
Final: {"answer": 407.65, "unit": "K"}

Answer: 407.65

Prompt: Convert 134.5 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 134.5 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=214 degrees and keep the unit as newtons.
Final: {"answer": [-120.625, -81.3626], "unit": "N"}

Answer: -120.625

Answer: -81.3626

Prompt: A vector has magnitude 145.5 N at 214 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=214 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": [-8.55, -19.5], "unit": "dimensionless"}

Answer: -8.55

Answer: -19.5

Prompt: A line passes through points (2, -36.6) and (9.25, -98.5875). 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 model card equation case 791740, 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
import math

def unit_vector_006622(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_006622"}

Answer: python_code

Prompt: Write a Python function unit_vector_006622(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_006622(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid laboratory survey records in release 208030, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 24.95 kg and a = 9.05 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 225.7975, "unit": "N"}

Answer: 225.7975

Prompt: A cart has mass 24.95 kg and measured acceleration 9.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 24.95 kg and a = 9.05 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 = 1.6^2 and multiply by 0.5 * 9.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 11.968, "unit": "J"}

Answer: 11.968

Prompt: A body of mass 9.35 kg moves at 1.6 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 1.6^2 and multiply by 0.5 * 9.35.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=79 degrees through the sine of 2 theta.
3. Substitute v=40.8 m/s and g=9.81 m/s^2.
Final: {"answer": 63.5663, "unit": "m"}

Answer: 63.5663

Prompt: A projectile is launched on level ground with no air resistance at speed 40.8 m/s and angle 79 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=79 degrees through the sine of 2 theta.
Substitute v=40.8 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.46 * 8.314 * 474 / 31.0.
Final: {"answer": 694.0956, "unit": "kPa"}

Answer: 694.0956

Prompt: An ideal gas sample has n=5.46 mol, T=474 K, and V=31.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.46 * 8.314 * 474 / 31.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1920 * 3.275 * 19.
Final: {"answer": 119472.0, "unit": "J"}

Answer: 119472.0

Prompt: A 1920 g sample has specific heat 3.275 J/(g*K). How much heat is needed to raise its temperature by 19 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1920 * 3.275 * 19.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=750 mg, t=329.5 h, and T_half=59.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 16.1441, "unit": "mg"}

Answer: 16.1441

Prompt: A radioactive sample starts with 750 mg. Its half-life is 59.5 hours. How many mg remain after 329.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=750 mg, t=329.5 h, and T_half=59.5 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 = 7.28 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 728.6334, "unit": "g"}

Answer: 728.6334

Prompt: A sample contains 7.28 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 = 7.28 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 4760 mL to 4.76 L.
3. Compute M = 4.56 / 4.76.
Final: {"answer": 0.958, "unit": "mol/L"}

Answer: 0.958

Prompt: A solution contains 4.56 mol of solute in 4760 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4760 mL to 4.76 L.
Compute M = 4.56 / 4.76.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(0)=-19 and f(3.6)=-44.2.
3. The interval width is 3.6.
Final: {"answer": -113.76, "unit": "area_units"}

Answer: -113.76

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7x+-19 from x=0 to x=3.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(0)=-19 and f(3.6)=-44.2.
The interval width is 3.6.


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": [0.959, -0.088, 0.394], "unit": "temperature_units"}

Answer: 0.959

Answer: -0.088

Answer: 0.394

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=-1.6, right=1.05; current interior values are [1.75, -0.55, 0.45]. 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 27536.0 / 1000.
Final: {"answer": 27.536, "unit": "kg"}

Answer: 27.536

Prompt: Convert 27536 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 27536.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=178 degrees and keep the unit as newtons.
Final: {"answer": [-36.4778, 1.2738], "unit": "N"}

Answer: -36.4778

Answer: 1.2738

Prompt: A vector has magnitude 36.5 N at 178 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=178 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": [-7.3, -22.75], "unit": "dimensionless"}

Answer: -7.3

Answer: -22.75

Prompt: A line passes through points (-2.5, -4.5) and (2.75, -42.825). 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 model card equation case 125157, 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 finite_differences_006640(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_006640"}

Answer: python_code

Prompt: Write a Python function finite_differences_006640(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_006640([5]) == []

assert finite_differences_006640([]) == []


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 44.5 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 6.15 kg and a = 15.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 92.865, "unit": "N"}

Answer: 92.865

Prompt: A cart has mass 6.15 kg and measured acceleration 15.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 6.15 kg and a = 15.1 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 31.95^2 and multiply by 0.5 * 28.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 14699.556, "unit": "J"}

Answer: 14699.556

Prompt: A body of mass 28.8 kg moves at 31.95 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 31.95^2 and multiply by 0.5 * 28.8.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=47 degrees through the sine of 2 theta.
3. Substitute v=20.3 m/s and g=9.81 m/s^2.
Final: {"answer": 41.9048, "unit": "m"}

Answer: 41.9048

Prompt: A projectile is launched on level ground with no air resistance at speed 20.3 m/s and angle 47 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=47 degrees through the sine of 2 theta.
Substitute v=20.3 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 = 4.16 * 8.314 * 277 / 14.1.
Final: {"answer": 679.4602, "unit": "kPa"}

Answer: 679.4602

Prompt: An ideal gas sample has n=4.16 mol, T=277 K, and V=14.1 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 = 4.16 * 8.314 * 277 / 14.1.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=198.7 V and R=118.5 ohm.
Final: {"answer": 333.1788, "unit": "W"}

Answer: 333.1788

Prompt: A resistor has resistance 118.5 ohm and voltage 198.7 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=198.7 V and R=118.5 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.69 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 390.9636, "unit": "g"}

Answer: 390.9636

Prompt: A sample contains 6.69 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.69 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 3885 mL to 3.885 L.
3. Compute M = 4.95 / 3.885.
Final: {"answer": 1.2741, "unit": "mol/L"}

Answer: 1.2741

Prompt: A solution contains 4.95 mol of solute in 3885 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3885 mL to 3.885 L.
Compute M = 4.95 / 3.885.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 0.0076, "unit": "state_units"}

Answer: 0.0076

Prompt: Use explicit Euler on dy/dt = -0.63 y with y(0)=15, step size h=1.05, for 7 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.
Apply that update for 7 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=0.2 and add it to the current value.
Final: {"answer": [1.01, 1.63, 0.54], "unit": "temperature_units"}

Answer: 1.01

Answer: 1.63

Answer: 0.54

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=2.85; current interior values are [1.4, 2.55, -0.9]. Use r=0.2. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.2 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 2386.5 / 100.
Final: {"answer": 23.865, "unit": "m"}

Answer: 23.865

Prompt: Convert 2386.5 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 2386.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=328 degrees and keep the unit as newtons.
Final: {"answer": [312.0817, -195.0103], "unit": "N"}

Answer: 312.0817

Answer: -195.0103

Prompt: A vector has magnitude 368 N at 328 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=328 degrees and keep the unit as newtons.


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

Answer: consistent

Prompt: In field worksheet case 799716, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def normalize_006658(values):
    total = sum(values)
    if total == 0:
        raise ValueError('cannot normalize zero-sum values')
    return [v / total for v in values]
```
Final: {"answer": "python_code", "function": "normalize_006658"}

Answer: python_code

Prompt: Write a Python function normalize_006658(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.

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

out = normalize_006658([2, 3, 5]); assert len(out) == 3

try:
    normalize_006658([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 mobile clinical record from batch 951128 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 11.65^2 and multiply by 0.5 * 24.45.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1659.2076, "unit": "J"}

Answer: 1659.2076

Prompt: A body of mass 24.45 kg moves at 11.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 11.65^2 and multiply by 0.5 * 24.45.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.75 * 8.314 * 601 / 36.4.
Final: {"answer": 240.2266, "unit": "kPa"}

Answer: 240.2266

Prompt: An ideal gas sample has n=1.75 mol, T=601 K, and V=36.4 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 = 1.75 * 8.314 * 601 / 36.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 695 * 1.375 * 94.
Final: {"answer": 89828.75, "unit": "J"}

Answer: 89828.75

Prompt: A 695 g sample has specific heat 1.375 J/(g*K). How much heat is needed to raise its temperature by 94 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 695 * 1.375 * 94.


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=192.1 V and R=39 ohm.
Final: {"answer": 946.2156, "unit": "W"}

Answer: 946.2156

Prompt: A resistor has resistance 39 ohm and voltage 192.1 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=192.1 V and R=39 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=538 mg, t=23 h, and T_half=43 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 371.3353, "unit": "mg"}

Answer: 371.3353

Prompt: A radioactive sample starts with 538 mg. Its half-life is 43 hours. How many mg remain after 23 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=538 mg, t=23 h, and T_half=43 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) = -1 y, so each step multiplies y by 1 - h*1.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": -0.6858, "unit": "state_units"}

Answer: -0.6858

Prompt: Use explicit Euler on dy/dt = -1 y with y(0)=24.5, step size h=1.6, for 7 steps. What is y after the final step?

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


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(7.4)=13.76 and f(8.6)=19.04.
3. The interval width is 1.2.
Final: {"answer": 19.68, "unit": "area_units"}

Answer: 19.68

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.4x+-18.8 from x=7.4 to x=8.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7.4)=13.76 and f(8.6)=19.04.
The interval width is 1.2.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -30.0 + 273.15.
Final: {"answer": 243.15, "unit": "K"}

Answer: 243.15

Prompt: Convert -30 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 -30.0 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=11 degrees and keep the unit as newtons.
Final: {"answer": [213.9947, 41.5964], "unit": "N"}

Answer: 213.9947

Answer: 41.5964

Prompt: A vector has magnitude 218 N at 11 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=11 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [3.35, -3.5], "unit": "dimensionless"}

Answer: 3.35

Answer: -3.5

Prompt: A line passes through points (10.25, 30.8375) and (18.75, 59.3125). 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. 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 517571, 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 weighted_sum_006676(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_006676"}

Answer: python_code

Prompt: Write a Python function weighted_sum_006676(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_006676([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: 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 43.4 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 = 7.35 kg and a = 2.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 18.0075, "unit": "N"}

Answer: 18.0075

Prompt: A cart has mass 7.35 kg and measured acceleration 2.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 7.35 kg and a = 2.45 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 30.9^2 and multiply by 0.5 * 23.5.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 11219.0175, "unit": "J"}

Answer: 11219.0175

Prompt: A body of mass 23.5 kg moves at 30.9 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 30.9^2 and multiply by 0.5 * 23.5.
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=68 degrees through the sine of 2 theta.
3. Substitute v=53.1 m/s and g=9.81 m/s^2.
Final: {"answer": 199.6601, "unit": "m"}

Answer: 199.6601

Prompt: A projectile is launched on level ground with no air resistance at speed 53.1 m/s and angle 68 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=68 degrees through the sine of 2 theta.
Substitute v=53.1 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 = 1575 * 2.785 * 6.
Final: {"answer": 26318.25, "unit": "J"}

Answer: 26318.25

Prompt: A 1575 g sample has specific heat 2.785 J/(g*K). How much heat is needed to raise its temperature by 6 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1575 * 2.785 * 6.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=125 V and R=33.9 ohm.
Final: {"answer": 460.9145, "unit": "W"}

Answer: 460.9145

Prompt: A resistor has resistance 33.9 ohm and voltage 125 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=125 V and R=33.9 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.16 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 316.2749, "unit": "g"}

Answer: 316.2749

Prompt: A sample contains 3.16 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 = 3.16 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 2015 mL to 2.015 L.
3. Compute M = 4.655 / 2.015.
Final: {"answer": 2.3102, "unit": "mol/L"}

Answer: 2.3102

Prompt: A solution contains 4.655 mol of solute in 2015 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2015 mL to 2.015 L.
Compute M = 4.655 / 2.015.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.83 y, so each step multiplies y by 1 - h*0.83.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.0027, "unit": "state_units"}

Answer: 0.0027

Prompt: Use explicit Euler on dy/dt = -0.83 y with y(0)=36, step size h=1.75, 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) = -0.83 y, so each step multiplies y by 1 - h*0.83.
Apply that update for 12 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-1.1)=10.58 and f(7.3)=37.46.
3. The interval width is 8.4.
Final: {"answer": 201.768, "unit": "area_units"}

Answer: 201.768

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.2x+14.1 from x=-1.1 to x=7.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-1.1)=10.58 and f(7.3)=37.46.
The interval width is 8.4.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.26 and add it to the current value.
Final: {"answer": [1.061, 0.95, 0.912], "unit": "temperature_units"}

Answer: 1.061

Answer: 0.95

Answer: 0.912

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0, right=0.35; current interior values are [2.4, -0.35, 1.9]. 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. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=225 degrees and keep the unit as newtons.
Final: {"answer": [-13.0815, -13.0815], "unit": "N"}

Answer: -13.0815

Answer: -13.0815

Prompt: A vector has magnitude 18.5 N at 225 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=225 degrees and keep the unit as newtons.


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

Answer: inconsistent

Prompt: In quality-control check case 682808, 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
import math

def unit_vector_006694(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_006694"}

Answer: python_code

Prompt: Write a Python function unit_vector_006694(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_006694(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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 routing scoring problem with 3026 items and budget 80945, 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 = 20.55 kg and a = 12 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 246.6, "unit": "N"}

Answer: 246.6

Prompt: A cart has mass 20.55 kg and measured acceleration 12 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 = 20.55 kg and a = 12 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 = 18.4^2 and multiply by 0.5 * 9.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1523.52, "unit": "J"}

Answer: 1523.52

Prompt: A body of mass 9 kg moves at 18.4 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 18.4^2 and multiply by 0.5 * 9.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=19 degrees through the sine of 2 theta.
3. Substitute v=80.2 m/s and g=9.81 m/s^2.
Final: {"answer": 403.6656, "unit": "m"}

Answer: 403.6656

Prompt: A projectile is launched on level ground with no air resistance at speed 80.2 m/s and angle 19 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=19 degrees through the sine of 2 theta.
Substitute v=80.2 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.21 * 8.314 * 519 / 16.8.
Final: {"answer": 1338.1531, "unit": "kPa"}

Answer: 1338.1531

Prompt: An ideal gas sample has n=5.21 mol, T=519 K, and V=16.8 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 = 5.21 * 8.314 * 519 / 16.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1315 * 0.895 * 108.
Final: {"answer": 127107.9, "unit": "J"}

Answer: 127107.9

Prompt: A 1315 g sample has specific heat 0.895 J/(g*K). How much heat is needed to raise its temperature by 108 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1315 * 0.895 * 108.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=59.7 V and R=44.3 ohm.
Final: {"answer": 80.4535, "unit": "W"}

Answer: 80.4535

Prompt: A resistor has resistance 44.3 ohm and voltage 59.7 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=59.7 V and R=44.3 ohm.