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

Answer: consistent

Prompt: In sensor calibration case 262844, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def center_values_003112(values):
    if not values:
        raise ValueError('center_values requires at least one value')
    mean = sum(values) / len(values)
    return [value - mean for value in values]
```
Final: {"answer": "python_code", "function": "center_values_003112"}

Answer: python_code

Prompt: Write a Python function center_values_003112(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.

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

try:
    center_values_003112([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=31 and h=1.95, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 1.05 kg and a = 14.95 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 15.6975, "unit": "N"}

Answer: 15.6975

Prompt: A cart has mass 1.05 kg and measured acceleration 14.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 1.05 kg and a = 14.95 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 18.75^2 and multiply by 0.5 * 21.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3752.9297, "unit": "J"}

Answer: 3752.9297

Prompt: A body of mass 21.35 kg moves at 18.75 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 18.75^2 and multiply by 0.5 * 21.35.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=43 degrees through the sine of 2 theta.
3. Substitute v=45.6 m/s and g=9.81 m/s^2.
Final: {"answer": 211.447, "unit": "m"}

Answer: 211.447

Prompt: A projectile is launched on level ground with no air resistance at speed 45.6 m/s and angle 43 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=43 degrees through the sine of 2 theta.
Substitute v=45.6 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 = 50 * 2.89 * 82.
Final: {"answer": 11849.0, "unit": "J"}

Answer: 11849.0

Prompt: A 50 g sample has specific heat 2.89 J/(g*K). How much heat is needed to raise its temperature by 82 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 50 * 2.89 * 82.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=168.4 V and R=50.6 ohm.
Final: {"answer": 560.4458, "unit": "W"}

Answer: 560.4458

Prompt: A resistor has resistance 50.6 ohm and voltage 168.4 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=168.4 V and R=50.6 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=783 mg, t=312.5 h, and T_half=63.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 25.8413, "unit": "mg"}

Answer: 25.8413

Prompt: A radioactive sample starts with 783 mg. Its half-life is 63.5 hours. How many mg remain after 312.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=783 mg, t=312.5 h, and T_half=63.5 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1155 mL to 1.155 L.
3. Compute M = 2.36 / 1.155.
Final: {"answer": 2.0433, "unit": "mol/L"}

Answer: 2.0433

Prompt: A solution contains 2.36 mol of solute in 1155 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1155 mL to 1.155 L.
Compute M = 2.36 / 1.155.


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 12 steps and round the final state.
Final: {"answer": 0.0001, "unit": "state_units"}

Answer: 0.0001

Prompt: Use explicit Euler on dy/dt = -0.93 y with y(0)=17.5, step size h=1.45, 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) = -0.93 y, so each step multiplies y by 1 - h*0.93.
Apply that update for 12 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(0.7)=-2.72 and f(4)=-24.5.
3. The interval width is 3.3.
Final: {"answer": -44.913, "unit": "area_units"}

Answer: -44.913

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.6x+1.9 from x=0.7 to x=4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(0.7)=-2.72 and f(4)=-24.5.
The interval width is 3.3.

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


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.28 and add it to the current value.
Final: {"answer": [0.556, -0.352, 0.506], "unit": "temperature_units"}

Answer: 0.556

Answer: -0.352

Answer: 0.506

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=2.5, right=2.4; current interior values are [0.85, -1.85, 0.8]. 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. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=306 degrees and keep the unit as newtons.
Final: {"answer": [165.4615, -227.7383], "unit": "N"}

Answer: 165.4615

Answer: -227.7383

Prompt: A vector has magnitude 281.5 N at 306 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=306 degrees and keep the unit as newtons.

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


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [0.35, 13.5], "unit": "dimensionless"}

Answer: 0.35

Answer: 13.5

Prompt: A line passes through points (12.25, 17.7875) and (22.25, 21.2875). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In instrument manual case 3024, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def normalize_003130(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_003130"}

Answer: python_code

Prompt: Write a Python function normalize_003130(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_003130([2, 3, 5]); assert len(out) == 3

try:
    normalize_003130([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 20.75 kg and a = 2.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 43.575, "unit": "N"}

Answer: 43.575

Prompt: A cart has mass 20.75 kg and measured acceleration 2.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 20.75 kg and a = 2.1 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 3.2^2 and multiply by 0.5 * 22.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 116.992, "unit": "J"}

Answer: 116.992

Prompt: A body of mass 22.85 kg moves at 3.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 3.2^2 and multiply by 0.5 * 22.85.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=28 degrees through the sine of 2 theta.
3. Substitute v=37 m/s and g=9.81 m/s^2.
Final: {"answer": 115.6934, "unit": "m"}

Answer: 115.6934

Prompt: A projectile is launched on level ground with no air resistance at speed 37 m/s and angle 28 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=28 degrees through the sine of 2 theta.
Substitute v=37 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.75 * 8.314 * 593 / 5.8.
Final: {"answer": 4037.6654, "unit": "kPa"}

Answer: 4037.6654

Prompt: An ideal gas sample has n=4.75 mol, T=593 K, and V=5.8 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 = 4.75 * 8.314 * 593 / 5.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1000 * 2.65 * 10.
Final: {"answer": 26500.0, "unit": "J"}

Answer: 26500.0

Prompt: A 1000 g sample has specific heat 2.65 J/(g*K). How much heat is needed to raise its temperature by 10 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1000 * 2.65 * 10.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.35 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 603.5226, "unit": "g"}

Answer: 603.5226

Prompt: A sample contains 3.35 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 3.35 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 940 mL to 0.94 L.
3. Compute M = 3 / 0.94.
Final: {"answer": 3.1915, "unit": "mol/L"}

Answer: 3.1915

Prompt: A solution contains 3 mol of solute in 940 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 940 mL to 0.94 L.
Compute M = 3 / 0.94.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.55 y, so each step multiplies y by 1 - h*0.55.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 24.1036, "unit": "state_units"}

Answer: 24.1036

Prompt: Use explicit Euler on dy/dt = -0.55 y with y(0)=48.5, step size h=0.2, 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) = -0.55 y, so each step multiplies y by 1 - h*0.55.
Apply that update for 6 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=0.36 and add it to the current value.
Final: {"answer": [0.996, 1.082, -0.438], "unit": "temperature_units"}

Answer: 0.996

Answer: 1.082

Answer: -0.438

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1, right=-1.95; current interior values are [2.85, 1.55, -1.05]. Use r=0.36. 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=0.36 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 36999.0 / 1000.
Final: {"answer": 36.999, "unit": "kg"}

Answer: 36.999

Prompt: Convert 36999 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 36999.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=198 degrees and keep the unit as newtons.
Final: {"answer": [-389.9332, -126.697], "unit": "N"}

Answer: -389.9332

Answer: -126.697

Prompt: A vector has magnitude 410 N at 198 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=198 degrees and keep the unit as newtons.


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

Answer: consistent

Prompt: In lab notebook case 120274, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def threshold_flags_003148(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_003148"}

Answer: python_code

Prompt: Write a Python function threshold_flags_003148(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.

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

assert threshold_flags_003148([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_003148([], 5) == []

assert threshold_flags_003148([-1, 0], 0) == [False, True]


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

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 55.8 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 1.6 kg and a = 4.7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 7.52, "unit": "N"}

Answer: 7.52

Prompt: A cart has mass 1.6 kg and measured acceleration 4.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 1.6 kg and a = 4.7 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 33.35^2 and multiply by 0.5 * 19.55.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 10871.9749, "unit": "J"}

Answer: 10871.9749

Prompt: A body of mass 19.55 kg moves at 33.35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 33.35^2 and multiply by 0.5 * 19.55.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=68 degrees through the sine of 2 theta.
3. Substitute v=63.4 m/s and g=9.81 m/s^2.
Final: {"answer": 284.6301, "unit": "m"}

Answer: 284.6301

Prompt: A projectile is launched on level ground with no air resistance at speed 63.4 m/s and angle 68 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=68 degrees through the sine of 2 theta.
Substitute v=63.4 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 5.92 * 8.314 * 527 / 106.5.
Final: {"answer": 243.5526, "unit": "kPa"}

Answer: 243.5526

Prompt: An ideal gas sample has n=5.92 mol, T=527 K, and V=106.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 5.92 * 8.314 * 527 / 106.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1895 * 2.745 * 17.
Final: {"answer": 88430.175, "unit": "J"}

Answer: 88430.175

Prompt: A 1895 g sample has specific heat 2.745 J/(g*K). How much heat is needed to raise its temperature by 17 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1895 * 2.745 * 17.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=611 mg, t=170.5 h, and T_half=59.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 83.8351, "unit": "mg"}

Answer: 83.8351

Prompt: A radioactive sample starts with 611 mg. Its half-life is 59.5 hours. How many mg remain after 170.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=611 mg, t=170.5 h, and T_half=59.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.05 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 305.2654, "unit": "g"}

Answer: 305.2654

Prompt: A sample contains 3.05 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 3.05 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.93 y, so each step multiplies y by 1 - h*0.93.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": -26.4425, "unit": "state_units"}

Answer: -26.4425

Prompt: Use explicit Euler on dy/dt = -0.93 y with y(0)=76, step size h=2, for 7 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.93 y, so each step multiplies y by 1 - h*0.93.
Apply that update for 7 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 18.0 + 273.15.
Final: {"answer": 291.15, "unit": "K"}

Answer: 291.15

Prompt: Convert 18 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 18.0 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=236 degrees and keep the unit as newtons.
Final: {"answer": [-176.4254, -261.5614], "unit": "N"}

Answer: -176.4254

Answer: -261.5614

Prompt: A vector has magnitude 315.5 N at 236 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=236 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [8.45, 1.25], "unit": "dimensionless"}

Answer: 8.45

Answer: 1.25

Prompt: A line passes through points (13.5, 115.325) and (22.25, 189.262). 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 weighted_sum_003166(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_003166"}

Answer: python_code

Prompt: Write a Python function weighted_sum_003166(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_003166([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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=0.28 and interior values [-1.45, 1.75, -0.6], but gives no boundary values. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 8.95 kg and a = 10 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 89.5, "unit": "N"}

Answer: 89.5

Prompt: A cart has mass 8.95 kg and measured acceleration 10 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 = 8.95 kg and a = 10 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=23 degrees through the sine of 2 theta.
3. Substitute v=71.1 m/s and g=9.81 m/s^2.
Final: {"answer": 370.6844, "unit": "m"}

Answer: 370.6844

Prompt: A projectile is launched on level ground with no air resistance at speed 71.1 m/s and angle 23 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=23 degrees through the sine of 2 theta.
Substitute v=71.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1520 * 2.315 * 76.
Final: {"answer": 267428.8, "unit": "J"}

Answer: 267428.8

Prompt: A 1520 g sample has specific heat 2.315 J/(g*K). How much heat is needed to raise its temperature by 76 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1520 * 2.315 * 76.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=592.5 mg, t=306.5 h, and T_half=68 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 26.0519, "unit": "mg"}

Answer: 26.0519

Prompt: A radioactive sample starts with 592.5 mg. Its half-life is 68 hours. How many mg remain after 306.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=592.5 mg, t=306.5 h, and T_half=68 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.58 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 358.3115, "unit": "g"}

Answer: 358.3115

Prompt: A sample contains 3.58 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 3.58 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4035 mL to 4.035 L.
3. Compute M = 0.365 / 4.035.
Final: {"answer": 0.0905, "unit": "mol/L"}

Answer: 0.0905

Prompt: A solution contains 0.365 mol of solute in 4035 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4035 mL to 4.035 L.
Compute M = 0.365 / 4.035.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 0.9154, "unit": "state_units"}

Answer: 0.9154

Prompt: Use explicit Euler on dy/dt = -0.59 y with y(0)=15, step size h=0.5, 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) = -0.59 y, so each step multiplies y by 1 - h*0.59.
Apply that update for 8 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(3.9)=1.31 and f(5.4)=8.66.
3. The interval width is 1.5.
Final: {"answer": 7.4775, "unit": "area_units"}

Answer: 7.4775

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.9x+-17.8 from x=3.9 to x=5.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3.9)=1.31 and f(5.4)=8.66.
The interval width is 1.5.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.22 and add it to the current value.
Final: {"answer": [0.76, -0.055, 0.539], "unit": "temperature_units"}

Answer: 0.76

Answer: -0.055

Answer: 0.539

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.65, right=-1.5; current interior values are [1.75, -1.65, 2.2]. 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. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=257 degrees and keep the unit as newtons.
Final: {"answer": [-2.5869, -11.2053], "unit": "N"}

Answer: -2.5869

Answer: -11.2053

Prompt: A vector has magnitude 11.5 N at 257 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=257 degrees and keep the unit as newtons.


Response:
Reasoning:
1. 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 field worksheet case 265775, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def threshold_flags_003184(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_003184"}

Answer: python_code

Prompt: Write a Python function threshold_flags_003184(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.

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

assert threshold_flags_003184([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_003184([], 5) == []

assert threshold_flags_003184([-1, 0], 0) == [False, True]


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

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 78.9 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. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 27.65^2 and multiply by 0.5 * 20.7.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 7912.8079, "unit": "J"}

Answer: 7912.8079

Prompt: A body of mass 20.7 kg moves at 27.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 27.65^2 and multiply by 0.5 * 20.7.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=51 degrees through the sine of 2 theta.
3. Substitute v=9.6 m/s and g=9.81 m/s^2.
Final: {"answer": 9.1892, "unit": "m"}

Answer: 9.1892

Prompt: A projectile is launched on level ground with no air resistance at speed 9.6 m/s and angle 51 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=51 degrees through the sine of 2 theta.
Substitute v=9.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.84 * 8.314 * 535 / 87.4.
Final: {"answer": 93.6419, "unit": "kPa"}

Answer: 93.6419

Prompt: An ideal gas sample has n=1.84 mol, T=535 K, and V=87.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.84 * 8.314 * 535 / 87.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1555 * 2.63 * 100.
Final: {"answer": 408965.0, "unit": "J"}

Answer: 408965.0

Prompt: A 1555 g sample has specific heat 2.63 J/(g*K). How much heat is needed to raise its temperature by 100 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1555 * 2.63 * 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=10.3 V and R=155.8 ohm.
Final: {"answer": 0.6809, "unit": "W"}

Answer: 0.6809

Prompt: A resistor has resistance 155.8 ohm and voltage 10.3 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=10.3 V and R=155.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=83.5 mg, t=308 h, and T_half=23 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0078, "unit": "mg"}

Answer: 0.0078

Prompt: A radioactive sample starts with 83.5 mg. Its half-life is 23 hours. How many mg remain after 308 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=83.5 mg, t=308 h, and T_half=23 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.92 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 16.5738, "unit": "g"}

Answer: 16.5738

Prompt: A sample contains 0.92 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.92 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1475 mL to 1.475 L.
3. Compute M = 4.66 / 1.475.
Final: {"answer": 3.1593, "unit": "mol/L"}

Answer: 3.1593

Prompt: A solution contains 4.66 mol of solute in 1475 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1475 mL to 1.475 L.
Compute M = 4.66 / 1.475.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.48 and add it to the current value.
Final: {"answer": [0.456, -0.338, -0.292], "unit": "temperature_units"}

Answer: 0.456

Answer: -0.338

Answer: -0.292

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.05, right=-0.55; current interior values are [-0.6, -0.05, -0.1]. Use r=0.48. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.48 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 31118.0 / 1000.
Final: {"answer": 31.118, "unit": "kg"}

Answer: 31.118

Prompt: Convert 31118 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 31118.0 / 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": [-5.9, 2.0], "unit": "dimensionless"}

Answer: -5.9

Answer: 2.0

Prompt: A line passes through points (9.25, -52.575) and (17, -98.3). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. 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 672739, 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 center_values_003202(values):
    if not values:
        raise ValueError('center_values requires at least one value')
    mean = sum(values) / len(values)
    return [value - mean for value in values]
```
Final: {"answer": "python_code", "function": "center_values_003202"}

Answer: python_code

Prompt: Write a Python function center_values_003202(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.

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

try:
    center_values_003202([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each mobile sensor record from batch 850165 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 24.5 kg and a = 10.4 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 254.8, "unit": "N"}

Answer: 254.8

Prompt: A cart has mass 24.5 kg and measured acceleration 10.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 24.5 kg and a = 10.4 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=42 degrees through the sine of 2 theta.
3. Substitute v=62.9 m/s and g=9.81 m/s^2.
Final: {"answer": 401.0944, "unit": "m"}

Answer: 401.0944

Prompt: A projectile is launched on level ground with no air resistance at speed 62.9 m/s and angle 42 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=42 degrees through the sine of 2 theta.
Substitute v=62.9 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1170 * 0.605 * 75.
Final: {"answer": 53088.75, "unit": "J"}

Answer: 53088.75

Prompt: A 1170 g sample has specific heat 0.605 J/(g*K). How much heat is needed to raise its temperature by 75 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1170 * 0.605 * 75.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=59.1 V and R=3.2 ohm.
Final: {"answer": 1091.5031, "unit": "W"}

Answer: 1091.5031

Prompt: A resistor has resistance 3.2 ohm and voltage 59.1 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=59.1 V and R=3.2 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=16 mg, t=126.5 h, and T_half=45 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 2.2798, "unit": "mg"}

Answer: 2.2798

Prompt: A radioactive sample starts with 16 mg. Its half-life is 45 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=16 mg, t=126.5 h, and T_half=45 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 2290 mL to 2.29 L.
3. Compute M = 0.485 / 2.29.
Final: {"answer": 0.2118, "unit": "mol/L"}

Answer: 0.2118

Prompt: A solution contains 0.485 mol of solute in 2290 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2290 mL to 2.29 L.
Compute M = 0.485 / 2.29.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.3)=-53.81 and f(11.5)=-61.95.
3. The interval width is 2.2.
Final: {"answer": -127.336, "unit": "area_units"}

Answer: -127.336

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.7x+-19.4 from x=9.3 to x=11.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.3)=-53.81 and f(11.5)=-61.95.
The interval width is 2.2.


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=0.28 and add it to the current value.
Final: {"answer": [1.336, 0.834, 0.448], "unit": "temperature_units"}

Answer: 1.336

Answer: 0.834

Answer: 0.448

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.15, right=0.55; current interior values are [0.3, 2.15, -0.7]. 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -36.5 + 273.15.
Final: {"answer": 236.65, "unit": "K"}

Answer: 236.65

Prompt: Convert -36.5 degC to K. Return the converted value with unit.

Kelvin equals Celsius plus 273.15.
Apply the conversion factor directly to the given value.
Compute -36.5 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=31 degrees and keep the unit as newtons.
Final: {"answer": [202.2915, 121.549], "unit": "N"}

Answer: 202.2915

Answer: 121.549

Prompt: A vector has magnitude 236 N at 31 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=31 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-1.2, 15.75], "unit": "dimensionless"}

Answer: -1.2

Answer: 15.75

Prompt: A line passes through points (12.5, 0.75) and (15, -2.25). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In instrument manual case 824079, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
def weighted_sum_003220(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_003220"}

Answer: python_code

Prompt: Write a Python function weighted_sum_003220(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_003220([1], [1, 2])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 17.95 kg and a = 2.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 43.9775, "unit": "N"}

Answer: 43.9775

Prompt: A cart has mass 17.95 kg and measured acceleration 2.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 17.95 kg and a = 2.45 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 30.6^2 and multiply by 0.5 * 21.55.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 10089.279, "unit": "J"}

Answer: 10089.279

Prompt: A body of mass 21.55 kg moves at 30.6 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 30.6^2 and multiply by 0.5 * 21.55.
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 = 2000 * 0.83 * 119.
Final: {"answer": 197540.0, "unit": "J"}

Answer: 197540.0

Prompt: A 2000 g sample has specific heat 0.83 J/(g*K). How much heat is needed to raise its temperature by 119 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 2000 * 0.83 * 119.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=235.1 V and R=44.3 ohm.
Final: {"answer": 1247.6752, "unit": "W"}

Answer: 1247.6752

Prompt: A resistor has resistance 44.3 ohm and voltage 235.1 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=235.1 V and R=44.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=394.5 mg, t=35 h, and T_half=109 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 315.781, "unit": "mg"}

Answer: 315.781

Prompt: A radioactive sample starts with 394.5 mg. Its half-life is 109 hours. How many mg remain after 35 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=394.5 mg, t=35 h, and T_half=109 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.48 y, so each step multiplies y by 1 - h*0.48.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 0.0059, "unit": "state_units"}

Answer: 0.0059

Prompt: Use explicit Euler on dy/dt = -0.48 y with y(0)=73.5, step size h=1.2, 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) = -0.48 y, so each step multiplies y by 1 - h*0.48.
Apply that update for 11 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 6354.0 / 1000.
Final: {"answer": 6.354, "unit": "kg"}

Answer: 6.354

Prompt: Convert 6354 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 6354.0 / 1000.


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 quality-control check case 438247, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.

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

Answer: inconsistent


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

```python
def threshold_flags_003238(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_003238"}

Answer: python_code

Prompt: Write a Python function threshold_flags_003238(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.

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

assert threshold_flags_003238([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_003238([], 5) == []

assert threshold_flags_003238([-1, 0], 0) == [False, True]


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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)=24 and h=1.2, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 9.15^2 and multiply by 0.5 * 20.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 837.225, "unit": "J"}

Answer: 837.225

Prompt: A body of mass 20 kg moves at 9.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 9.15^2 and multiply by 0.5 * 20.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=84 degrees through the sine of 2 theta.
3. Substitute v=56.1 m/s and g=9.81 m/s^2.
Final: {"answer": 66.7015, "unit": "m"}

Answer: 66.7015

Prompt: A projectile is launched on level ground with no air resistance at speed 56.1 m/s and angle 84 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=84 degrees through the sine of 2 theta.
Substitute v=56.1 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 = 0.4 * 8.314 * 552 / 8.6.
Final: {"answer": 213.4571, "unit": "kPa"}

Answer: 213.4571

Prompt: An ideal gas sample has n=0.4 mol, T=552 K, and V=8.6 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 = 0.4 * 8.314 * 552 / 8.6.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=471 mg, t=247 h, and T_half=42 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 7.9924, "unit": "mg"}

Answer: 7.9924

Prompt: A radioactive sample starts with 471 mg. Its half-life is 42 hours. How many mg remain after 247 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=471 mg, t=247 h, and T_half=42 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 = 1.06 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 46.6506, "unit": "g"}

Answer: 46.6506

Prompt: A sample contains 1.06 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.06 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4925 mL to 4.925 L.
3. Compute M = 2.485 / 4.925.
Final: {"answer": 0.5046, "unit": "mol/L"}

Answer: 0.5046

Prompt: A solution contains 2.485 mol of solute in 4925 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4925 mL to 4.925 L.
Compute M = 2.485 / 4.925.


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 3 steps and round the final state.
Final: {"answer": 29.3939, "unit": "state_units"}

Answer: 29.3939

Prompt: Use explicit Euler on dy/dt = -0.41 y with y(0)=58.5, step size h=0.5, for 3 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.
Apply that update for 3 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(0.1)=-18.56 and f(8.9)=-23.84.
3. The interval width is 8.8.
Final: {"answer": -186.56, "unit": "area_units"}

Answer: -186.56

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.6x+-18.5 from x=0.1 to x=8.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(0.1)=-18.56 and f(8.9)=-23.84.
The interval width is 8.8.


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=0.28 and add it to the current value.
Final: {"answer": [-0.282, 0.28, 0.486], "unit": "temperature_units"}

Answer: -0.282

Answer: 0.28

Answer: 0.486

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.65, right=0.15; current interior values are [1.3, -1.4, 1.9]. 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. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=126 degrees and keep the unit as newtons.
Final: {"answer": [-187.2096, 257.6719], "unit": "N"}

Answer: -187.2096

Answer: 257.6719

Prompt: A vector has magnitude 318.5 N at 126 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=126 degrees and keep the unit as newtons.


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

Answer: consistent

Prompt: In sensor calibration case 685333, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

```python
import math

def unit_vector_003256(x, y):
    norm = math.hypot(x, y)
    if norm == 0:
        raise ValueError('zero vector has no direction')
    return (x / norm, y / norm)
```
Final: {"answer": "python_code", "function": "unit_vector_003256"}

Answer: python_code

Prompt: Write a Python function unit_vector_003256(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.

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

try:
    unit_vector_003256(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a allocation scoring problem with 1101 items and budget 58785, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 24 kg and a = 0.2 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 4.8, "unit": "N"}

Answer: 4.8

Prompt: A cart has mass 24 kg and measured acceleration 0.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 24 kg and a = 0.2 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 5.1^2 and multiply by 0.5 * 10.95.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 142.4047, "unit": "J"}

Answer: 142.4047

Prompt: A body of mass 10.95 kg moves at 5.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 5.1^2 and multiply by 0.5 * 10.95.
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=12 degrees through the sine of 2 theta.
3. Substitute v=17.6 m/s and g=9.81 m/s^2.
Final: {"answer": 12.8431, "unit": "m"}

Answer: 12.8431

Prompt: A projectile is launched on level ground with no air resistance at speed 17.6 m/s and angle 12 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=12 degrees through the sine of 2 theta.
Substitute v=17.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.19 * 8.314 * 599 / 71.8.
Final: {"answer": 82.539, "unit": "kPa"}

Answer: 82.539

Prompt: An ideal gas sample has n=1.19 mol, T=599 K, and V=71.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.19 * 8.314 * 599 / 71.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 935 * 3.515 * 111.
Final: {"answer": 364804.275, "unit": "J"}

Answer: 364804.275

Prompt: A 935 g sample has specific heat 3.515 J/(g*K). How much heat is needed to raise its temperature by 111 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 935 * 3.515 * 111.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=237.2 V and R=97.6 ohm.
Final: {"answer": 576.4738, "unit": "W"}

Answer: 576.4738

Prompt: A resistor has resistance 97.6 ohm and voltage 237.2 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=237.2 V and R=97.6 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=149.5 mg, t=268.5 h, and T_half=108 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 26.6838, "unit": "mg"}

Answer: 26.6838

Prompt: A radioactive sample starts with 149.5 mg. Its half-life is 108 hours. How many mg remain after 268.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=149.5 mg, t=268.5 h, and T_half=108 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.59 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 466.604, "unit": "g"}

Answer: 466.604

Prompt: A sample contains 2.59 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 2.59 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4660 mL to 4.66 L.
3. Compute M = 1.835 / 4.66.
Final: {"answer": 0.3938, "unit": "mol/L"}

Answer: 0.3938

Prompt: A solution contains 1.835 mol of solute in 4660 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4660 mL to 4.66 L.
Compute M = 1.835 / 4.66.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.24 y, so each step multiplies y by 1 - h*0.24.
3. Apply that update for 10 steps and round the final state.
Final: {"answer": 37.1834, "unit": "state_units"}

Answer: 37.1834

Prompt: Use explicit Euler on dy/dt = -0.24 y with y(0)=78.5, step size h=0.3, 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) = -0.24 y, so each step multiplies y by 1 - h*0.24.
Apply that update for 10 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(7.1)=-46.6 and f(10)=-58.2.
3. The interval width is 2.9.
Final: {"answer": -151.96, "unit": "area_units"}

Answer: -151.96

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-4x+-18.2 from x=7.1 to x=10. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7.1)=-46.6 and f(10)=-58.2.
The interval width is 2.9.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.22 and add it to the current value.
Final: {"answer": [-0.112, 0.142, 1.067], "unit": "temperature_units"}

Answer: -0.112

Answer: 0.142

Answer: 1.067

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=2.9, right=-0.65; current interior values are [-1.3, -0.1, 2.2]. 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 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 2138.5 / 100.
Final: {"answer": 21.385, "unit": "m"}

Answer: 21.385

Prompt: Convert 2138.5 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 2138.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=314 degrees and keep the unit as newtons.
Final: {"answer": [36.4696, -37.7653], "unit": "N"}

Answer: 36.4696

Answer: -37.7653

Prompt: A vector has magnitude 52.5 N at 314 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=314 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-4.25, 30.0], "unit": "dimensionless"}

Answer: -4.25

Answer: 30.0

Prompt: A line passes through points (9.25, -9.3125) and (9.75, -11.4375). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In instrument manual case 783226, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: 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)=65 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. Use Newton's second law F = m a.
2. Substitute m = 18.8 kg and a = 0.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 4.7, "unit": "N"}

Answer: 4.7

Prompt: A cart has mass 18.8 kg and measured acceleration 0.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 18.8 kg and a = 0.25 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 15.35^2 and multiply by 0.5 * 26.95.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 3175.0132, "unit": "J"}

Answer: 3175.0132

Prompt: A body of mass 26.95 kg moves at 15.35 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 15.35^2 and multiply by 0.5 * 26.95.
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=61 degrees through the sine of 2 theta.
3. Substitute v=30.2 m/s and g=9.81 m/s^2.
Final: {"answer": 78.8434, "unit": "m"}

Answer: 78.8434

Prompt: A projectile is launched on level ground with no air resistance at speed 30.2 m/s and angle 61 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=61 degrees through the sine of 2 theta.
Substitute v=30.2 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1905 * 2.815 * 49.
Final: {"answer": 262766.175, "unit": "J"}

Answer: 262766.175

Prompt: A 1905 g sample has specific heat 2.815 J/(g*K). How much heat is needed to raise its temperature by 49 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1905 * 2.815 * 49.


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=107.2 V and R=119.3 ohm.
Final: {"answer": 96.3272, "unit": "W"}

Answer: 96.3272

Prompt: A resistor has resistance 119.3 ohm and voltage 107.2 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=107.2 V and R=119.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=477 mg, t=200.5 h, and T_half=77.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 79.3825, "unit": "mg"}

Answer: 79.3825

Prompt: A radioactive sample starts with 477 mg. Its half-life is 77.5 hours. How many mg remain after 200.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=477 mg, t=200.5 h, and T_half=77.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.4 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 432.456, "unit": "g"}

Answer: 432.456

Prompt: A sample contains 7.4 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 = 7.4 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 975 mL to 0.975 L.
3. Compute M = 1.31 / 0.975.
Final: {"answer": 1.3436, "unit": "mol/L"}

Answer: 1.3436

Prompt: A solution contains 1.31 mol of solute in 975 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 975 mL to 0.975 L.
Compute M = 1.31 / 0.975.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.9 y, so each step multiplies y by 1 - h*0.9.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 1.3594, "unit": "state_units"}

Answer: 1.3594

Prompt: Use explicit Euler on dy/dt = -0.9 y with y(0)=66, step size h=0.6, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.9 y, so each step multiplies y by 1 - h*0.9.
Apply that update for 5 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.34 and add it to the current value.
Final: {"answer": [-0.864, -0.271, 0.913], "unit": "temperature_units"}

Answer: -0.864

Answer: -0.271

Answer: 0.913

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=1.7; current interior values are [-1.85, -0.05, 1.1]. Use r=0.34. Return the next interior vector.

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


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4049.5 / 100.
Final: {"answer": 40.495, "unit": "m"}

Answer: 40.495

Prompt: Convert 4049.5 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 4049.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=120 degrees and keep the unit as newtons.
Final: {"answer": [-101.75, 176.2362], "unit": "N"}

Answer: -101.75

Answer: 176.2362

Prompt: A vector has magnitude 203.5 N at 120 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=120 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. velocity divided by time is acceleration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In sensor calibration case 76001, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
velocity divided by time is acceleration
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


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

```python
def clamp_003292(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_003292"}

Answer: python_code

Prompt: Write a Python function clamp_003292(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_003292(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 20.2 kg and a = 0.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 5.05, "unit": "N"}

Answer: 5.05

Prompt: A cart has mass 20.2 kg and measured acceleration 0.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 20.2 kg and a = 0.25 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 34^2 and multiply by 0.5 * 1.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 780.3, "unit": "J"}

Answer: 780.3

Prompt: A body of mass 1.35 kg moves at 34 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 34^2 and multiply by 0.5 * 1.35.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=34 degrees through the sine of 2 theta.
3. Substitute v=8 m/s and g=9.81 m/s^2.
Final: {"answer": 6.0489, "unit": "m"}

Answer: 6.0489

Prompt: A projectile is launched on level ground with no air resistance at speed 8 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=8 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.87 * 8.314 * 282 / 28.5.
Final: {"answer": 71.5704, "unit": "kPa"}

Answer: 71.5704

Prompt: An ideal gas sample has n=0.87 mol, T=282 K, and V=28.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.87 * 8.314 * 282 / 28.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 40 * 0.75 * 115.
Final: {"answer": 3450.0, "unit": "J"}

Answer: 3450.0

Prompt: A 40 g sample has specific heat 0.75 J/(g*K). How much heat is needed to raise its temperature by 115 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 40 * 0.75 * 115.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=238.9 V and R=36.2 ohm.
Final: {"answer": 1576.608, "unit": "W"}

Answer: 1576.608

Prompt: A resistor has resistance 36.2 ohm and voltage 238.9 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=238.9 V and R=36.2 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=814 mg, t=39.5 h, and T_half=51.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 478.3407, "unit": "mg"}

Answer: 478.3407

Prompt: A radioactive sample starts with 814 mg. Its half-life is 51.5 hours. How many mg remain after 39.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=814 mg, t=39.5 h, and T_half=51.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.98 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 175.1598, "unit": "g"}

Answer: 175.1598

Prompt: A sample contains 3.98 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 3.98 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 115 mL to 0.115 L.
3. Compute M = 1.535 / 0.115.
Final: {"answer": 13.3478, "unit": "mol/L"}

Answer: 13.3478

Prompt: A solution contains 1.535 mol of solute in 115 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 115 mL to 0.115 L.
Compute M = 1.535 / 0.115.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.39 y, so each step multiplies y by 1 - h*0.39.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 3.0955, "unit": "state_units"}

Answer: 3.0955

Prompt: Use explicit Euler on dy/dt = -0.39 y with y(0)=43, step size h=0.65, 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) = -0.39 y, so each step multiplies y by 1 - h*0.39.
Apply that update for 9 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.06 and add it to the current value.
Final: {"answer": [-0.096, -0.048, 1.157], "unit": "temperature_units"}

Answer: -0.096

Answer: -0.048

Answer: 1.157

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.45, right=-1.1; current interior values are [0.0, -0.15, 1.4]. Use r=0.06. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 4675.0 / 1000.
Final: {"answer": 4.675, "unit": "kg"}

Answer: 4.675

Prompt: Convert 4675 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 4675.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=109 degrees and keep the unit as newtons.
Final: {"answer": [-87.415, 253.8717], "unit": "N"}

Answer: -87.415

Answer: 253.8717

Prompt: A vector has magnitude 268.5 N at 109 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=109 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-3.65, -29.25], "unit": "dimensionless"}

Answer: -3.65

Answer: -29.25

Prompt: A line passes through points (18.25, -95.8625) and (30.5, -140.575). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a alignment scoring problem with 4503 items and budget 8290, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 22.1 kg and a = 1.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 38.675, "unit": "N"}

Answer: 38.675

Prompt: A cart has mass 22.1 kg and measured acceleration 1.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 22.1 kg and a = 1.75 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 13.45^2 and multiply by 0.5 * 14.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1266.3175, "unit": "J"}

Answer: 1266.3175

Prompt: A body of mass 14 kg moves at 13.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 13.45^2 and multiply by 0.5 * 14.
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=56 degrees through the sine of 2 theta.
3. Substitute v=58.5 m/s and g=9.81 m/s^2.
Final: {"answer": 323.4511, "unit": "m"}

Answer: 323.4511

Prompt: A projectile is launched on level ground with no air resistance at speed 58.5 m/s and angle 56 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=56 degrees through the sine of 2 theta.
Substitute v=58.5 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 235 * 4.135 * 107.
Final: {"answer": 103974.575, "unit": "J"}

Answer: 103974.575

Prompt: A 235 g sample has specific heat 4.135 J/(g*K). How much heat is needed to raise its temperature by 107 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 235 * 4.135 * 107.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=684 mg, t=34.5 h, and T_half=106.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 546.436, "unit": "mg"}

Answer: 546.436

Prompt: A radioactive sample starts with 684 mg. Its half-life is 106.5 hours. How many mg remain after 34.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=684 mg, t=34.5 h, and T_half=106.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.6 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 160.1392, "unit": "g"}

Answer: 160.1392

Prompt: A sample contains 1.6 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.6 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2040 mL to 2.04 L.
3. Compute M = 4.72 / 2.04.
Final: {"answer": 2.3137, "unit": "mol/L"}

Answer: 2.3137

Prompt: A solution contains 4.72 mol of solute in 2040 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2040 mL to 2.04 L.
Compute M = 4.72 / 2.04.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 13.6826, "unit": "state_units"}

Answer: 13.6826

Prompt: Use explicit Euler on dy/dt = -0.21 y with y(0)=39, step size h=0.9, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.
Apply that update for 5 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.46 and add it to the current value.
Final: {"answer": [-0.379, 0.341, -0.389], "unit": "temperature_units"}

Answer: -0.379

Answer: 0.341

Answer: -0.389

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1, right=-0.7; current interior values are [1.3, -0.05, -0.55]. Use r=0.46. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.46 and add it to the current value.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 143.0 + 273.15.
Final: {"answer": 416.15, "unit": "K"}

Answer: 416.15

Prompt: Convert 143 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 143.0 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=297 degrees and keep the unit as newtons.
Final: {"answer": [147.7739, -290.0226], "unit": "N"}

Answer: 147.7739

Answer: -290.0226

Prompt: A vector has magnitude 325.5 N at 297 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=297 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [1.8, -5.75], "unit": "dimensionless"}

Answer: 1.8

Answer: -5.75

Prompt: A line passes through points (4.5, 2.35) and (6.75, 6.4). 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. grams cancel with J/(g*K), and kelvin cancels, leaving joules
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In instrument manual case 820179, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


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

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=1.28 mol and T=304 K, but does not give volume. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 12.2 kg and a = 14.9 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 181.78, "unit": "N"}

Answer: 181.78

Prompt: A cart has mass 12.2 kg and measured acceleration 14.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 12.2 kg and a = 14.9 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 = 4.82 * 8.314 * 550 / 68.9.
Final: {"answer": 319.8899, "unit": "kPa"}

Answer: 319.8899

Prompt: An ideal gas sample has n=4.82 mol, T=550 K, and V=68.9 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 = 4.82 * 8.314 * 550 / 68.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 255 * 4.51 * 12.
Final: {"answer": 13800.6, "unit": "J"}

Answer: 13800.6

Prompt: A 255 g sample has specific heat 4.51 J/(g*K). How much heat is needed to raise its temperature by 12 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 255 * 4.51 * 12.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=956 mg, t=303 h, and T_half=46 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 9.9446, "unit": "mg"}

Answer: 9.9446

Prompt: A radioactive sample starts with 956 mg. Its half-life is 46 hours. How many mg remain after 303 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=956 mg, t=303 h, and T_half=46 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.49 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 145.5156, "unit": "g"}

Answer: 145.5156

Prompt: A sample contains 2.49 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 = 2.49 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 675 mL to 0.675 L.
3. Compute M = 2.795 / 0.675.
Final: {"answer": 4.1407, "unit": "mol/L"}

Answer: 4.1407

Prompt: A solution contains 2.795 mol of solute in 675 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 675 mL to 0.675 L.
Compute M = 2.795 / 0.675.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-0.7)=-13.01 and f(5.1)=29.33.
3. The interval width is 5.8.
Final: {"answer": 47.328, "unit": "area_units"}

Answer: 47.328

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=7.3x+-7.9 from x=-0.7 to x=5.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-0.7)=-13.01 and f(5.1)=29.33.
The interval width is 5.8.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 494.0 / 100.
Final: {"answer": 4.94, "unit": "m"}

Answer: 4.94

Prompt: Convert 494 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 494.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=284 degrees and keep the unit as newtons.
Final: {"answer": [6.6529, -26.6831], "unit": "N"}

Answer: 6.6529

Answer: -26.6831

Prompt: A vector has magnitude 27.5 N at 284 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=284 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-6.95, -4.0], "unit": "dimensionless"}

Answer: -6.95

Answer: -4.0

Prompt: A line passes through points (11.25, -82.1875) and (22, -156.9). 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.