Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4350 mL to 4.35 L.
3. Compute M = 2.955 / 4.35.
Final: {"answer": 0.6793, "unit": "mol/L"}

Answer: 0.6793

Prompt: A solution contains 2.955 mol of solute in 4350 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4350 mL to 4.35 L.
Compute M = 2.955 / 4.35.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 26634.0 / 1000.
Final: {"answer": 26.634, "unit": "kg"}

Answer: 26.634

Prompt: Convert 26634 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 26634.0 / 1000.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 295 * 3.35 * 5.
Final: {"answer": 4941.25, "unit": "J"}

Answer: 4941.25

Prompt: A 295 g sample has specific heat 3.35 J/(g*K). How much heat is needed to raise its temperature by 5 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 295 * 3.35 * 5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 310 * 4.39 * 103.
Final: {"answer": 140172.7, "unit": "J"}

Answer: 140172.7

Prompt: A 310 g sample has specific heat 4.39 J/(g*K). How much heat is needed to raise its temperature by 103 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 310 * 4.39 * 103.


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=40.2 V and R=134.9 ohm.
Final: {"answer": 11.9795, "unit": "W"}

Answer: 11.9795

Prompt: A resistor has resistance 134.9 ohm and voltage 40.2 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=40.2 V and R=134.9 ohm.


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": [7.85, -20.25], "unit": "dimensionless"}

Answer: 7.85

Answer: -20.25

Prompt: A line passes through points (14.25, 91.6125) and (20.75, 142.637). 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. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=190.4 V and R=104.3 ohm.
Final: {"answer": 347.5758, "unit": "W"}

Answer: 347.5758

Prompt: A resistor has resistance 104.3 ohm and voltage 190.4 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=190.4 V and R=104.3 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.98 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 176.5529, "unit": "g"}

Answer: 176.5529

Prompt: A sample contains 0.98 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.98 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-9.7)=-52.52 and f(-5.6)=-25.46.
3. The interval width is 4.1.
Final: {"answer": -159.859, "unit": "area_units"}

Answer: -159.859

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.6x+11.5 from x=-9.7 to x=-5.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.7)=-52.52 and f(-5.6)=-25.46.
The interval width is 4.1.

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


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.66 * 8.314 * 378 / 40.3.
Final: {"answer": 51.4684, "unit": "kPa"}

Answer: 51.4684

Prompt: An ideal gas sample has n=0.66 mol, T=378 K, and V=40.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.66 * 8.314 * 378 / 40.3.


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

Answer: consistent

Prompt: In quality-control check case 174408, 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. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: recurrence, objective, tie_breaking_rule.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a scheduler scoring problem with 285 items and budget 38560, 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. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.4 and add it to the current value.
Final: {"answer": [1.28, 0.11, 1.39], "unit": "temperature_units"}

Answer: 1.28

Answer: 0.11

Answer: 1.39

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=3; current interior values are [0.9, 1.05, -1.15]. Use r=0.4. Return the next interior vector.

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


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.76 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 136.9186, "unit": "g"}

Answer: 136.9186

Prompt: A sample contains 0.76 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.76 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [1.55, 10.75], "unit": "dimensionless"}

Answer: 1.55

Answer: 10.75

Prompt: A line passes through points (16.5, 36.325) and (22.25, 45.2375). 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 running_total_002086(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_002086"}

Answer: python_code

Prompt: Write a Python function running_total_002086(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 21.5^2 and multiply by 0.5 * 5.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1236.5187, "unit": "J"}

Answer: 1236.5187

Prompt: A body of mass 5.35 kg moves at 21.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 21.5^2 and multiply by 0.5 * 5.35.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1080 * 4.91 * 2.
Final: {"answer": 10605.6, "unit": "J"}

Answer: 10605.6

Prompt: A 1080 g sample has specific heat 4.91 J/(g*K). How much heat is needed to raise its temperature by 2 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1080 * 4.91 * 2.


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_002158(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_002158"}

Answer: python_code

Prompt: Write a Python function finite_differences_002158(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_002158([5]) == []

assert finite_differences_002158([]) == []


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 8.9 kg and a = 12.8 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 113.92, "unit": "N"}

Answer: 113.92

Prompt: A cart has mass 8.9 kg and measured acceleration 12.8 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 = 8.9 kg and a = 12.8 m/s^2.
The unit kg*m/s^2 is one newton.


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=161.6 V and R=75.6 ohm.
Final: {"answer": 345.4307, "unit": "W"}

Answer: 345.4307

Prompt: A resistor has resistance 75.6 ohm and voltage 161.6 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=161.6 V and R=75.6 ohm.


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)=5.5 and h=1.9, 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. 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_002248(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_002248"}

Answer: python_code

Prompt: Write a Python function running_total_002248(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: left_boundary, right_boundary.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.18 and interior values [-0.2, 1.55, 2.05], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use 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 = 2.51 * 8.314 * 332 / 17.8.
Final: {"answer": 389.226, "unit": "kPa"}

Answer: 389.226

Prompt: An ideal gas sample has n=2.51 mol, T=332 K, and V=17.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.51 * 8.314 * 332 / 17.8.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.38 y, so each step multiplies y by 1 - h*0.38.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.38 y with y(0)=2.5, step size h=1.95, for 9 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.38 y, so each step multiplies y by 1 - h*0.38.
Apply that update for 9 steps and round the final state.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 14066.0 / 1000.
Final: {"answer": 14.066, "unit": "kg"}

Answer: 14.066

Prompt: Convert 14066 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 14066.0 / 1000.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-1.9, 10.25], "unit": "dimensionless"}

Answer: -1.9

Answer: 10.25

Prompt: A line passes through points (6.5, -2.1) and (7, -3.05). 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. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=17 degrees through the sine of 2 theta.
3. Substitute v=39.9 m/s and g=9.81 m/s^2.
Final: {"answer": 90.7483, "unit": "m"}

Answer: 90.7483

Prompt: A projectile is launched on level ground with no air resistance at speed 39.9 m/s and angle 17 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=17 degrees through the sine of 2 theta.
Substitute v=39.9 m/s and g=9.81 m/s^2.

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


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1720 * 4.075 * 2.
Final: {"answer": 14018.0, "unit": "J"}

Answer: 14018.0

Prompt: A 1720 g sample has specific heat 4.075 J/(g*K). How much heat is needed to raise its temperature by 2 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1720 * 4.075 * 2.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.58 y with y(0)=77.5, step size h=1.4, 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) = -0.58 y, so each step multiplies y by 1 - h*0.58.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 1.8^2 and multiply by 0.5 * 20.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 32.886, "unit": "J"}

Answer: 32.886

Prompt: A body of mass 20.3 kg moves at 1.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 1.8^2 and multiply by 0.5 * 20.3.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2090 mL to 2.09 L.
3. Compute M = 0.025 / 2.09.
Final: {"answer": 0.012, "unit": "mol/L"}

Answer: 0.012

Prompt: A solution contains 0.025 mol of solute in 2090 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2090 mL to 2.09 L.
Compute M = 0.025 / 2.09.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.96 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 231.4224, "unit": "g"}

Answer: 231.4224

Prompt: A sample contains 3.96 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 3.96 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 0.2633, "unit": "state_units"}

Answer: 0.2633

Prompt: Use explicit Euler on dy/dt = -0.78 y with y(0)=60.5, step size h=0.5, for 11 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.
Apply that update for 11 steps and round the final state.


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=146.6 V and R=183.5 ohm.
Final: {"answer": 117.1202, "unit": "W"}

Answer: 117.1202

Prompt: A resistor has resistance 183.5 ohm and voltage 146.6 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=146.6 V and R=183.5 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.91 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 216.0891, "unit": "g"}

Answer: 216.0891

Prompt: A sample contains 4.91 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 = 4.91 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


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_002428(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_002428"}

Answer: python_code

Prompt: Write a Python function clamp_002428(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_002428(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=7 degrees through the sine of 2 theta.
3. Substitute v=64.7 m/s and g=9.81 m/s^2.
Final: {"answer": 103.2321, "unit": "m"}

Answer: 103.2321

Prompt: A projectile is launched on level ground with no air resistance at speed 64.7 m/s and angle 7 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=7 degrees through the sine of 2 theta.
Substitute v=64.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.22 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 622.5411, "unit": "g"}

Answer: 622.5411

Prompt: A sample contains 6.22 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 = 6.22 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 1595 mL to 1.595 L.
3. Compute M = 3.68 / 1.595.
Final: {"answer": 2.3072, "unit": "mol/L"}

Answer: 2.3072

Prompt: A solution contains 3.68 mol of solute in 1595 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1595 mL to 1.595 L.
Compute M = 3.68 / 1.595.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 10.7 kg and a = 14.35 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 153.545, "unit": "N"}

Answer: 153.545

Prompt: A cart has mass 10.7 kg and measured acceleration 14.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 10.7 kg and a = 14.35 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=491 mg, t=7.5 h, and T_half=64.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 452.9789, "unit": "mg"}

Answer: 452.9789

Prompt: A radioactive sample starts with 491 mg. Its half-life is 64.5 hours. How many mg remain after 7.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=491 mg, t=7.5 h, and T_half=64.5 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 290 * 2.66 * 88.
Final: {"answer": 67883.2, "unit": "J"}

Answer: 67883.2

Prompt: A 290 g sample has specific heat 2.66 J/(g*K). How much heat is needed to raise its temperature by 88 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 290 * 2.66 * 88.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=60 degrees through the sine of 2 theta.
3. Substitute v=48.6 m/s and g=9.81 m/s^2.
Final: {"answer": 208.5135, "unit": "m"}

Answer: 208.5135

Prompt: A projectile is launched on level ground with no air resistance at speed 48.6 m/s and angle 60 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=60 degrees through the sine of 2 theta.
Substitute v=48.6 m/s and g=9.81 m/s^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": [-0.063, -1.613, 1.991], "unit": "temperature_units"}

Answer: -0.063

Answer: -1.613

Answer: 1.991

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.95, right=-0.75; current interior values are [0.0, -2.0, 2.45]. 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. Use Newton's second law F = m a.
2. Substitute m = 18 kg and a = 9.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 171.9, "unit": "N"}

Answer: 171.9

Prompt: A cart has mass 18 kg and measured acceleration 9.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 18 kg and a = 9.55 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.4 y, so each step multiplies y by 1 - h*0.4.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 2.8072, "unit": "state_units"}

Answer: 2.8072

Prompt: Use explicit Euler on dy/dt = -0.4 y with y(0)=58, step size h=1.95, for 2 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.4 y, so each step multiplies y by 1 - h*0.4.
Apply that update for 2 steps and round the final state.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.02 y, so each step multiplies y by 1 - h*0.02.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 34.2245, "unit": "state_units"}

Answer: 34.2245

Prompt: Use explicit Euler on dy/dt = -0.02 y with y(0)=38.5, step size h=1.45, for 4 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.02 y, so each step multiplies y by 1 - h*0.02.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 19.1^2 and multiply by 0.5 * 25.65.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 4678.6883, "unit": "J"}

Answer: 4678.6883

Prompt: A body of mass 25.65 kg moves at 19.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 19.1^2 and multiply by 0.5 * 25.65.
The unit kg*m^2/s^2 is one joule.


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=154.9 V and R=159.3 ohm.
Final: {"answer": 150.6215, "unit": "W"}

Answer: 150.6215

Prompt: A resistor has resistance 159.3 ohm and voltage 154.9 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=154.9 V and R=159.3 ohm.


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 sensor calibration case 712839, 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. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3980 mL to 3.98 L.
3. Compute M = 3.6 / 3.98.
Final: {"answer": 0.9045, "unit": "mol/L"}

Answer: 0.9045

Prompt: A solution contains 3.6 mol of solute in 3980 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3980 mL to 3.98 L.
Compute M = 3.6 / 3.98.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 4.15 kg and a = 15.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 65.7775, "unit": "N"}

Answer: 65.7775

Prompt: A cart has mass 4.15 kg and measured acceleration 15.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 4.15 kg and a = 15.85 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 300 * 1.65 * 37.
Final: {"answer": 18315.0, "unit": "J"}

Answer: 18315.0

Prompt: A 300 g sample has specific heat 1.65 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 = 300 * 1.65 * 37.


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=170.2 V and R=75.9 ohm.
Final: {"answer": 381.6606, "unit": "W"}

Answer: 381.6606

Prompt: A resistor has resistance 75.9 ohm and voltage 170.2 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=170.2 V and R=75.9 ohm.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 14575.0 / 1000.
Final: {"answer": 14.575, "unit": "kg"}

Answer: 14.575

Prompt: Convert 14575 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 14575.0 / 1000.


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_002626(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_002626"}

Answer: python_code

Prompt: Write a Python function running_total_002626(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

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


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1610 * 0.865 * 68.
Final: {"answer": 94700.2, "unit": "J"}

Answer: 94700.2

Prompt: A 1610 g sample has specific heat 0.865 J/(g*K). How much heat is needed to raise its temperature by 68 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1610 * 0.865 * 68.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 4.75 kg and a = 15.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 73.625, "unit": "N"}

Answer: 73.625

Prompt: A cart has mass 4.75 kg and measured acceleration 15.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 4.75 kg and a = 15.5 m/s^2.
The unit kg*m/s^2 is one newton.


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 = 1.67 * 8.314 * 567 / 101.3.
Final: {"answer": 77.7142, "unit": "kPa"}

Answer: 77.7142

Prompt: An ideal gas sample has n=1.67 mol, T=567 K, and V=101.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.67 * 8.314 * 567 / 101.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 40 * 4.47 * 79.
Final: {"answer": 14125.2, "unit": "J"}

Answer: 14125.2

Prompt: A 40 g sample has specific heat 4.47 J/(g*K). How much heat is needed to raise its temperature by 79 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 40 * 4.47 * 79.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(0.4)=1.5 and f(1.3)=0.6.
3. The interval width is 0.9.
Final: {"answer": 0.945, "unit": "area_units"}

Answer: 0.945

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1x+1.9 from x=0.4 to x=1.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(0.4)=1.5 and f(1.3)=0.6.
The interval width is 0.9.


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": [-9.0, 19.0], "unit": "dimensionless"}

Answer: -9.0

Answer: 19.0

Prompt: A line passes through points (-6.75, 79.75) and (2.75, -5.75). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 595 * 2.57 * 66.
Final: {"answer": 100923.9, "unit": "J"}

Answer: 100923.9

Prompt: A 595 g sample has specific heat 2.57 J/(g*K). How much heat is needed to raise its temperature by 66 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 595 * 2.57 * 66.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -25.0 + 273.15.
Final: {"answer": 248.15, "unit": "K"}

Answer: 248.15

Prompt: Convert -25 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 -25.0 + 273.15.


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

```python
def weighted_sum_002716(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_002716"}

Answer: python_code

Prompt: Write a Python function weighted_sum_002716(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_002716([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1155 * 3.16 * 5.
Final: {"answer": 18249.0, "unit": "J"}

Answer: 18249.0

Prompt: A 1155 g sample has specific heat 3.16 J/(g*K). How much heat is needed to raise its temperature by 5 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1155 * 3.16 * 5.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1030 mL to 1.03 L.
3. Compute M = 0.725 / 1.03.
Final: {"answer": 0.7039, "unit": "mol/L"}

Answer: 0.7039

Prompt: A solution contains 0.725 mol of solute in 1030 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1030 mL to 1.03 L.
Compute M = 0.725 / 1.03.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 0.9981, "unit": "state_units"}

Answer: 0.9981

Prompt: Use explicit Euler on dy/dt = -0.41 y with y(0)=24, step size h=0.8, 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) = -0.41 y, so each step multiplies y by 1 - h*0.41.
Apply that update for 8 steps and round the final state.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [4.0, -4.75], "unit": "dimensionless"}

Answer: 4.0

Answer: -4.75

Prompt: A line passes through points (6.25, 20.25) and (8.75, 30.25). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. 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 48.3 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. 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 model card equation case 638988, 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 pairwise_ratios_002770(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_002770"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_002770(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_002770([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_002770([1, 2], [1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=281 degrees and keep the unit as newtons.
Final: {"answer": [83.956, -431.916], "unit": "N"}

Answer: 83.956

Answer: -431.916

Prompt: A vector has magnitude 440 N at 281 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=281 degrees and keep the unit as newtons.

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


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 77979, 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. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=21 degrees through the sine of 2 theta.
3. Substitute v=40.3 m/s and g=9.81 m/s^2.
Final: {"answer": 110.7776, "unit": "m"}

Answer: 110.7776

Prompt: A projectile is launched on level ground with no air resistance at speed 40.3 m/s and angle 21 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=21 degrees through the sine of 2 theta.
Substitute v=40.3 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=169.1 V and R=126.7 ohm.
Final: {"answer": 225.6891, "unit": "W"}

Answer: 225.6891

Prompt: A resistor has resistance 126.7 ohm and voltage 169.1 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=169.1 V and R=126.7 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.33 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 102.5433, "unit": "g"}

Answer: 102.5433

Prompt: A sample contains 2.33 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 = 2.33 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.25 y, so each step multiplies y by 1 - h*0.25.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 0.6503, "unit": "state_units"}

Answer: 0.6503

Prompt: Use explicit Euler on dy/dt = -0.25 y with y(0)=71.5, step size h=1.5, 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) = -0.25 y, so each step multiplies y by 1 - h*0.25.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4415.0 / 100.
Final: {"answer": 44.15, "unit": "m"}

Answer: 44.15

Prompt: Convert 4415 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 4415.0 / 100.


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=89.6 V and R=160.9 ohm.
Final: {"answer": 49.8953, "unit": "W"}

Answer: 49.8953

Prompt: A resistor has resistance 160.9 ohm and voltage 89.6 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=89.6 V and R=160.9 ohm.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.14 y, so each step multiplies y by 1 - h*0.14.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 72.6136, "unit": "state_units"}

Answer: 72.6136

Prompt: Use explicit Euler on dy/dt = -0.14 y with y(0)=79, step size h=0.05, 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) = -0.14 y, so each step multiplies y by 1 - h*0.14.
Apply that update for 12 steps and round the final state.


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

```python
def safe_mean_002842(values):
    if not values:
        raise ValueError('safe_mean requires at least one value')
    return sum(values) / len(values)
```
Final: {"answer": "python_code", "function": "safe_mean_002842"}

Answer: python_code

Prompt: Write a Python function safe_mean_002842(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.

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

try:
    safe_mean_002842([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-6.7)=12.18 and f(-0.8)=9.82.
3. The interval width is 5.9.
Final: {"answer": 64.9, "unit": "area_units"}

Answer: 64.9

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.4x+9.5 from x=-6.7 to x=-0.8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-6.7)=12.18 and f(-0.8)=9.82.
The interval width is 5.9.


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": [2.8, 6.75], "unit": "dimensionless"}

Answer: 2.8

Answer: 6.75

Prompt: A line passes through points (-11, -24.05) and (-4.5, -5.85). 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. 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 = 4.7 * 8.314 * 464 / 72.9.
Final: {"answer": 248.7129, "unit": "kPa"}

Answer: 248.7129

Prompt: An ideal gas sample has n=4.7 mol, T=464 K, and V=72.9 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 = 4.7 * 8.314 * 464 / 72.9.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=356.5 mg, t=126.5 h, and T_half=99 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 147.0314, "unit": "mg"}

Answer: 147.0314

Prompt: A radioactive sample starts with 356.5 mg. Its half-life is 99 hours. How many mg remain after 126.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=356.5 mg, t=126.5 h, and T_half=99 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 = 1.91 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 191.1662, "unit": "g"}

Answer: 191.1662

Prompt: A sample contains 1.91 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.91 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


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, -20.0], "unit": "dimensionless"}

Answer: 9.45

Answer: -20.0

Prompt: A line passes through points (6.75, 43.7875) and (10.25, 76.8625). 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. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 85 * 0.615 * 57.
Final: {"answer": 2979.675, "unit": "J"}

Answer: 2979.675

Prompt: A 85 g sample has specific heat 0.615 J/(g*K). How much heat is needed to raise its temperature by 57 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 85 * 0.615 * 57.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.93 y, so each step multiplies y by 1 - h*0.93.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.2898, "unit": "state_units"}

Answer: 0.2898

Prompt: Use explicit Euler on dy/dt = -0.93 y with y(0)=1, step size h=1.95, for 6 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.93 y, so each step multiplies y by 1 - h*0.93.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 115.0 + 273.15.
Final: {"answer": 388.15, "unit": "K"}

Answer: 388.15

Prompt: Convert 115 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 115.0 + 273.15.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 24.55^2 and multiply by 0.5 * 16.55.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 4987.3632, "unit": "J"}

Answer: 4987.3632

Prompt: A body of mass 16.55 kg moves at 24.55 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 24.55^2 and multiply by 0.5 * 16.55.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.42 and add it to the current value.
Final: {"answer": [1.312, 1.081, 0.454], "unit": "temperature_units"}

Answer: 1.312

Answer: 1.081

Answer: 0.454

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=1.3, right=-1.6; current interior values are [-0.2, 1.9, 2.05]. Use r=0.42. Return the next interior vector.

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


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=121 degrees and keep the unit as newtons.
Final: {"answer": [-222.754, 370.7249], "unit": "N"}

Answer: -222.754

Answer: 370.7249

Prompt: A vector has magnitude 432.5 N at 121 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=121 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(8.3)=-33.4 and f(16)=-48.8.
3. The interval width is 7.7.
Final: {"answer": -316.47, "unit": "area_units"}

Answer: -316.47

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2x+-16.8 from x=8.3 to x=16. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(8.3)=-33.4 and f(16)=-48.8.
The interval width is 7.7.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4290 mL to 4.29 L.
3. Compute M = 4.18 / 4.29.
Final: {"answer": 0.9744, "unit": "mol/L"}

Answer: 0.9744

Prompt: A solution contains 4.18 mol of solute in 4290 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4290 mL to 4.29 L.
Compute M = 4.18 / 4.29.


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": [-0.866, -0.292, 1.74], "unit": "temperature_units"}

Answer: -0.866

Answer: -0.292

Answer: 1.74

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=1.35, right=2.8; current interior values are [-2.0, -1.3, 3.0]. 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. Compare the dimensions on both sides of the equation.
2. amount times volume is not concentration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In simulation spec case 113615, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def running_total_003040(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_003040"}

Answer: python_code

Prompt: Write a Python function running_total_003040(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 12.15^2 and multiply by 0.5 * 0.95.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 70.1207, "unit": "J"}

Answer: 70.1207

Prompt: A body of mass 0.95 kg moves at 12.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 12.15^2 and multiply by 0.5 * 0.95.
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=37 degrees through the sine of 2 theta.
3. Substitute v=69.1 m/s and g=9.81 m/s^2.
Final: {"answer": 467.8738, "unit": "m"}

Answer: 467.8738

Prompt: A projectile is launched on level ground with no air resistance at speed 69.1 m/s and angle 37 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=37 degrees through the sine of 2 theta.
Substitute v=69.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.8 * 8.314 * 387 / 118.3.
Final: {"answer": 21.7584, "unit": "kPa"}

Answer: 21.7584

Prompt: An ideal gas sample has n=0.8 mol, T=387 K, and V=118.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.8 * 8.314 * 387 / 118.3.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.95 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 171.1482, "unit": "g"}

Answer: 171.1482

Prompt: A sample contains 0.95 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.95 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=262 degrees and keep the unit as newtons.
Final: {"answer": [-44.7442, -318.3712], "unit": "N"}

Answer: -44.7442

Answer: -318.3712

Prompt: A vector has magnitude 321.5 N at 262 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=262 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 75 * 3.92 * 5.
Final: {"answer": 1470.0, "unit": "J"}

Answer: 1470.0

Prompt: A 75 g sample has specific heat 3.92 J/(g*K). How much heat is needed to raise its temperature by 5 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 75 * 3.92 * 5.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 20.05^2 and multiply by 0.5 * 10.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2160.7634, "unit": "J"}

Answer: 2160.7634

Prompt: A body of mass 10.75 kg moves at 20.05 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 20.05^2 and multiply by 0.5 * 10.75.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.98 * 8.314 * 326 / 10.8.
Final: {"answer": 747.8597, "unit": "kPa"}

Answer: 747.8597

Prompt: An ideal gas sample has n=2.98 mol, T=326 K, and V=10.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.98 * 8.314 * 326 / 10.8.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.2 and add it to the current value.
Final: {"answer": [-0.47, 1.67, 2.08], "unit": "temperature_units"}

Answer: -0.47

Answer: 1.67

Answer: 2.08

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=1.95; current interior values are [-1.4, 2.6, 1.95]. 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 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 12611.0 / 1000.
Final: {"answer": 12.611, "unit": "kg"}

Answer: 12.611

Prompt: Convert 12611 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 12611.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=3 degrees and keep the unit as newtons.
Final: {"answer": [275.6218, 14.4447], "unit": "N"}

Answer: 275.6218

Answer: 14.4447

Prompt: A vector has magnitude 276 N at 3 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=3 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.09 * 8.314 * 254 / 4.3.
Final: {"answer": 2499.7298, "unit": "kPa"}

Answer: 2499.7298

Prompt: An ideal gas sample has n=5.09 mol, T=254 K, and V=4.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.09 * 8.314 * 254 / 4.3.


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

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.18 and interior values [-1.95, -1.5, -1.55], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=114.9 V and R=81.8 ohm.
Final: {"answer": 161.3938, "unit": "W"}

Answer: 161.3938

Prompt: A resistor has resistance 81.8 ohm and voltage 114.9 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=114.9 V and R=81.8 ohm.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(6.1)=-54.03 and f(9.8)=-77.34.
3. The interval width is 3.7.
Final: {"answer": -243.0345, "unit": "area_units"}

Answer: -243.0345

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.3x+-15.6 from x=6.1 to x=9.8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(6.1)=-54.03 and f(9.8)=-77.34.
The interval width is 3.7.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.32 and add it to the current value.
Final: {"answer": [0.78, 0.534, 0.14], "unit": "temperature_units"}

Answer: 0.78

Answer: 0.534

Answer: 0.14

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=-0.2, right=0.5; current interior values are [1.5, 0.95, -0.9]. Use r=0.32. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.32 and add it to the current value.


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

Answer: inconsistent

Prompt: In sensor calibration case 393800, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 25573.0 / 1000.
Final: {"answer": 25.573, "unit": "kg"}

Answer: 25.573

Prompt: Convert 25573 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 25573.0 / 1000.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.5)=-12.7 and f(10.6)=-15.12.
3. The interval width is 1.1.
Final: {"answer": -15.301, "unit": "area_units"}

Answer: -15.301

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.2x+8.2 from x=9.5 to x=10.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.5)=-12.7 and f(10.6)=-15.12.
The interval width is 1.1.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=300 degrees and keep the unit as newtons.
Final: {"answer": [7.5, -12.9904], "unit": "N"}

Answer: 7.5

Answer: -12.9904

Prompt: A vector has magnitude 15 N at 300 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=300 degrees and keep the unit as newtons.


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

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.42 and interior values [1.45, 0.35, -1.25], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3205 mL to 3.205 L.
3. Compute M = 4.96 / 3.205.
Final: {"answer": 1.5476, "unit": "mol/L"}

Answer: 1.5476

Prompt: A solution contains 4.96 mol of solute in 3205 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3205 mL to 3.205 L.
Compute M = 4.96 / 3.205.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 130 * 2.355 * 29.
Final: {"answer": 8878.35, "unit": "J"}

Answer: 8878.35

Prompt: A 130 g sample has specific heat 2.355 J/(g*K). How much heat is needed to raise its temperature by 29 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 130 * 2.355 * 29.


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": [8.0, 13.0], "unit": "dimensionless"}

Answer: 8.0

Answer: 13.0

Prompt: A line passes through points (-12.5, -87) and (-9.25, -61). 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 one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-2.5)=31.25 and f(7.3)=-16.77.
3. The interval width is 9.8.
Final: {"answer": 70.952, "unit": "area_units"}

Answer: 70.952

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.9x+19 from x=-2.5 to x=7.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-2.5)=31.25 and f(7.3)=-16.77.
The interval width is 9.8.


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 crop record from batch 582924 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. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(4.2)=41.46 and f(5.6)=50.28.
3. The interval width is 1.4.
Final: {"answer": 64.218, "unit": "area_units"}

Answer: 64.218

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.3x+15 from x=4.2 to x=5.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.2)=41.46 and f(5.6)=50.28.
The interval width is 1.4.


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

Answer: inconsistent

Prompt: In simulation spec case 4877, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.96 * 8.314 * 482 / 91.7.
Final: {"answer": 260.4558, "unit": "kPa"}

Answer: 260.4558

Prompt: An ideal gas sample has n=5.96 mol, T=482 K, and V=91.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.96 * 8.314 * 482 / 91.7.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=99.7 V and R=27.1 ohm.
Final: {"answer": 366.793, "unit": "W"}

Answer: 366.793

Prompt: A resistor has resistance 27.1 ohm and voltage 99.7 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=99.7 V and R=27.1 ohm.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 15.0591, "unit": "state_units"}

Answer: 15.0591

Prompt: Use explicit Euler on dy/dt = -0.15 y with y(0)=16.5, step size h=0.2, for 3 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.
Apply that update for 3 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=0.24 and add it to the current value.
Final: {"answer": [-0.336, -0.084, 1.348], "unit": "temperature_units"}

Answer: -0.336

Answer: -0.084

Answer: 1.348

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.15, right=2.4; current interior values are [-0.3, -0.9, 1.9]. 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. Compare the dimensions on both sides of the equation.
2. speed squared over acceleration has units of meters
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In model card equation case 185920, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=34 degrees through the sine of 2 theta.
3. Substitute v=60.3 m/s and g=9.81 m/s^2.
Final: {"answer": 343.662, "unit": "m"}

Answer: 343.662

Prompt: A projectile is launched on level ground with no air resistance at speed 60.3 m/s and angle 34 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=34 degrees through the sine of 2 theta.
Substitute v=60.3 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3330 mL to 3.33 L.
3. Compute M = 4.665 / 3.33.
Final: {"answer": 1.4009, "unit": "mol/L"}

Answer: 1.4009

Prompt: A solution contains 4.665 mol of solute in 3330 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3330 mL to 3.33 L.
Compute M = 4.665 / 3.33.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 1.0697, "unit": "state_units"}

Answer: 1.0697

Prompt: Use explicit Euler on dy/dt = -0.47 y with y(0)=59, step size h=0.65, for 11 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.
Apply that update for 11 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(5.6)=-10.94 and f(7.4)=-8.96.
3. The interval width is 1.8.
Final: {"answer": -17.91, "unit": "area_units"}

Answer: -17.91

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.1x+-17.1 from x=5.6 to x=7.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(5.6)=-10.94 and f(7.4)=-8.96.
The interval width is 1.8.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 5.55 kg and a = 4.05 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 22.4775, "unit": "N"}

Answer: 22.4775

Prompt: A cart has mass 5.55 kg and measured acceleration 4.05 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 = 5.55 kg and a = 4.05 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-9.1)=43.86 and f(-1.9)=17.94.
3. The interval width is 7.2.
Final: {"answer": 222.48, "unit": "area_units"}

Answer: 222.48

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.6x+11.1 from x=-9.1 to x=-1.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-9.1)=43.86 and f(-1.9)=17.94.
The interval width is 7.2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.57 * 8.314 * 379 / 73.6.
Final: {"answer": 24.4032, "unit": "kPa"}

Answer: 24.4032

Prompt: An ideal gas sample has n=0.57 mol, T=379 K, and V=73.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.57 * 8.314 * 379 / 73.6.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1005 mL to 1.005 L.
3. Compute M = 2.34 / 1.005.
Final: {"answer": 2.3284, "unit": "mol/L"}

Answer: 2.3284

Prompt: A solution contains 2.34 mol of solute in 1005 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1005 mL to 1.005 L.
Compute M = 2.34 / 1.005.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=104.6 V and R=9.5 ohm.
Final: {"answer": 1151.7011, "unit": "W"}

Answer: 1151.7011

Prompt: A resistor has resistance 9.5 ohm and voltage 104.6 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=104.6 V and R=9.5 ohm.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(5.3)=-24.07 and f(11.2)=-70.68.
3. The interval width is 5.9.
Final: {"answer": -279.5125, "unit": "area_units"}

Answer: -279.5125

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.9x+17.8 from x=5.3 to x=11.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(5.3)=-24.07 and f(11.2)=-70.68.
The interval width is 5.9.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1896.0 / 100.
Final: {"answer": 18.96, "unit": "m"}

Answer: 18.96

Prompt: Convert 1896 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 1896.0 / 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": [-2.5, -0.25], "unit": "dimensionless"}

Answer: -2.5

Answer: -0.25

Prompt: A line passes through points (-18.25, 45.375) and (-3.25, 7.875). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: inconsistent

Prompt: In student derivation case 593012, 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 weighted_sum_003472(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_003472"}

Answer: python_code

Prompt: Write a Python function weighted_sum_003472(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_003472([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=744 mg, t=63.5 h, and T_half=24 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 118.877, "unit": "mg"}

Answer: 118.877

Prompt: A radioactive sample starts with 744 mg. Its half-life is 24 hours. How many mg remain after 63.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=744 mg, t=63.5 h, and T_half=24 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1315 mL to 1.315 L.
3. Compute M = 2.73 / 1.315.
Final: {"answer": 2.076, "unit": "mol/L"}

Answer: 2.076

Prompt: A solution contains 2.73 mol of solute in 1315 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1315 mL to 1.315 L.
Compute M = 2.73 / 1.315.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 5.45^2 and multiply by 0.5 * 26.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 396.5284, "unit": "J"}

Answer: 396.5284

Prompt: A body of mass 26.7 kg moves at 5.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 5.45^2 and multiply by 0.5 * 26.7.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 7.7 kg and a = 13.05 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 100.485, "unit": "N"}

Answer: 100.485

Prompt: A cart has mass 7.7 kg and measured acceleration 13.05 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 = 7.7 kg and a = 13.05 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1855 * 0.985 * 73.
Final: {"answer": 133383.775, "unit": "J"}

Answer: 133383.775

Prompt: A 1855 g sample has specific heat 0.985 J/(g*K). How much heat is needed to raise its temperature by 73 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1855 * 0.985 * 73.


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": [8.25, 4.0], "unit": "dimensionless"}

Answer: 8.25

Answer: 4.0

Prompt: A line passes through points (-6.5, -49.625) and (4, 37). 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. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 20.85^2 and multiply by 0.5 * 16.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3553.8564, "unit": "J"}

Answer: 3553.8564

Prompt: A body of mass 16.35 kg moves at 20.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 20.85^2 and multiply by 0.5 * 16.35.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.68 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 168.1462, "unit": "g"}

Answer: 168.1462

Prompt: A sample contains 1.68 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.68 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 1295 mL to 1.295 L.
3. Compute M = 1.225 / 1.295.
Final: {"answer": 0.9459, "unit": "mol/L"}

Answer: 0.9459

Prompt: A solution contains 1.225 mol of solute in 1295 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1295 mL to 1.295 L.
Compute M = 1.225 / 1.295.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 27.75^2 and multiply by 0.5 * 6.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2367.9422, "unit": "J"}

Answer: 2367.9422

Prompt: A body of mass 6.15 kg moves at 27.75 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 27.75^2 and multiply by 0.5 * 6.15.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.22 and add it to the current value.
Final: {"answer": [1.683, 0.492, -0.669], "unit": "temperature_units"}

Answer: 1.683

Answer: 0.492

Answer: -0.669

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=2.65, right=-0.15; current interior values are [1.65, 0.8, -1.45]. Use r=0.22. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 43977.0 / 1000.
Final: {"answer": 43.977, "unit": "kg"}

Answer: 43.977

Prompt: Convert 43977 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 43977.0 / 1000.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 14.45^2 and multiply by 0.5 * 14.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1534.6984, "unit": "J"}

Answer: 1534.6984

Prompt: A body of mass 14.7 kg moves at 14.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 14.45^2 and multiply by 0.5 * 14.7.
The unit kg*m^2/s^2 is one joule.


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=41.3 V and R=132.7 ohm.
Final: {"answer": 12.8537, "unit": "W"}

Answer: 12.8537

Prompt: A resistor has resistance 132.7 ohm and voltage 41.3 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=41.3 V and R=132.7 ohm.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.04 y, so each step multiplies y by 1 - h*0.04.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 6.3584, "unit": "state_units"}

Answer: 6.3584

Prompt: Use explicit Euler on dy/dt = -0.04 y with y(0)=8.5, step size h=1.75, for 4 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.04 y, so each step multiplies y by 1 - h*0.04.
Apply that update for 4 steps and round the final state.


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": [2.3, -25.75], "unit": "dimensionless"}

Answer: 2.3

Answer: -25.75

Prompt: A line passes through points (7.75, -7.925) and (22, 24.85). 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. 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": [1.045, 1.68, 2.226], "unit": "temperature_units"}

Answer: 1.045

Answer: 1.68

Answer: 2.226

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.45, right=2.3; current interior values are [0.2, 2.2, 2.2]. 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. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2780 mL to 2.78 L.
3. Compute M = 4.99 / 2.78.
Final: {"answer": 1.795, "unit": "mol/L"}

Answer: 1.795

Prompt: A solution contains 4.99 mol of solute in 2780 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2780 mL to 2.78 L.
Compute M = 4.99 / 2.78.


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_003670(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_003670"}

Answer: python_code

Prompt: Write a Python function normalize_003670(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_003670([2, 3, 5]); assert len(out) == 3

try:
    normalize_003670([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=69 degrees through the sine of 2 theta.
3. Substitute v=57.2 m/s and g=9.81 m/s^2.
Final: {"answer": 223.169, "unit": "m"}

Answer: 223.169

Prompt: A projectile is launched on level ground with no air resistance at speed 57.2 m/s and angle 69 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=69 degrees through the sine of 2 theta.
Substitute v=57.2 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.39 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1331.3528, "unit": "g"}

Answer: 1331.3528

Prompt: A sample contains 7.39 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.39 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.75 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 43.83, "unit": "g"}

Answer: 43.83

Prompt: A sample contains 0.75 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.75 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


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": [5.0, -24.75], "unit": "dimensionless"}

Answer: 5.0

Answer: -24.75

Prompt: A line passes through points (-11.25, -81) and (-2.5, -37.25). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. 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_003778(values):
    return [values[i + 1] - values[i] for i in range(len(values) - 1)]
```
Final: {"answer": "python_code", "function": "finite_differences_003778"}

Answer: python_code

Prompt: Write a Python function finite_differences_003778(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_003778([5]) == []

assert finite_differences_003778([]) == []


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=321.5 mg, t=236 h, and T_half=56.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 17.7738, "unit": "mg"}

Answer: 17.7738

Prompt: A radioactive sample starts with 321.5 mg. Its half-life is 56.5 hours. How many mg remain after 236 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=321.5 mg, t=236 h, and T_half=56.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=185.5 V and R=46.1 ohm.
Final: {"answer": 746.4262, "unit": "W"}

Answer: 746.4262

Prompt: A resistor has resistance 46.1 ohm and voltage 185.5 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=185.5 V and R=46.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=519 mg, t=123.5 h, and T_half=20 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 7.183, "unit": "mg"}

Answer: 7.183

Prompt: A radioactive sample starts with 519 mg. Its half-life is 20 hours. How many mg remain after 123.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=519 mg, t=123.5 h, and T_half=20 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(3.8)=-39.28 and f(7.4)=-61.24.
3. The interval width is 3.6.
Final: {"answer": -180.936, "unit": "area_units"}

Answer: -180.936

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.1x+-16.1 from x=3.8 to x=7.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3.8)=-39.28 and f(7.4)=-61.24.
The interval width is 3.6.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3685 mL to 3.685 L.
3. Compute M = 4.52 / 3.685.
Final: {"answer": 1.2266, "unit": "mol/L"}

Answer: 1.2266

Prompt: A solution contains 4.52 mol of solute in 3685 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3685 mL to 3.685 L.
Compute M = 4.52 / 3.685.


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 model card equation case 328760, 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. Compare the dimensions on both sides of the equation.
2. velocity times time gives distance, not acceleration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In sensor calibration case 698046, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 7.85^2 and multiply by 0.5 * 10.4.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 320.437, "unit": "J"}

Answer: 320.437

Prompt: A body of mass 10.4 kg moves at 7.85 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 7.85^2 and multiply by 0.5 * 10.4.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1425 * 4.45 * 27.
Final: {"answer": 171213.75, "unit": "J"}

Answer: 171213.75

Prompt: A 1425 g sample has specific heat 4.45 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 = 1425 * 4.45 * 27.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 14.3 kg and a = 5.7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 81.51, "unit": "N"}

Answer: 81.51

Prompt: A cart has mass 14.3 kg and measured acceleration 5.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 14.3 kg and a = 5.7 m/s^2.
The unit kg*m/s^2 is one newton.