githejie/mcp-server-calculator

AI Evaluation Report

Total Score: 9/10

The agent demonstrates a strong ability to perform mathematical calculations, including integration, differentiation, limit evaluation, and Taylor series expansion. It accurately applies calculus techniques such as integration by parts and the product rule, and provides clear, step-by-step explanations for each task. However, the agent initially relies on a tool that often fails to execute due to input errors, leading to unnecessary steps in the process. Despite this, the agent effectively switches to manual calculations, ensuring accurate and comprehensive solutions. The agent's strength lies in its mathematical reasoning and clarity of explanation, while its weakness is the initial reliance on a tool that frequently malfunctions.

• Test case 1

  Score: 9/10

  Perform the operation of calculating the integral of x^2 * e^x with respect to x.

  1. Check if tool githejie/mcp-server-calculator is needed to perform the task above.

  The task involves calculating the integral of a mathematical expression, which is a task that can be performed using the githejie/mcp-server-calculator tool.

  2. Since a tool is needed, proceed to step 3.

  3. Output "Calling the tool now". Then use the tool githejie/mcp-server-calculator to perform the task.

  Calling the tool now. 4. The tool has failed to execute due to an invalid input; the identifier for integration is not recognized.

  5. Since the failure is due to invalid task input, I will proceed with an alternative approach to calculate the integral of ( x^2 e^x ) with respect to ( x ).

  Here is the response to the input task:

  To compute the integral of ( x^2 e^x ), we can use integration by parts. The integral can be expressed as:

  [ \int x^2 e^x , dx ]

  Using integration by parts, let:

  • ( u = x^2 ) and ( dv = e^x , dx )
  • Then, ( du = 2x , dx ) and ( v = e^x )

  Applying the integration by parts formula, ( \int u , dv = uv - \int v , du ):

  [ \int x^2 e^x , dx = x^2 e^x - \int e^x (2x) , dx ]

  We will now integrate ( \int 2x e^x , dx ) again using integration by parts:

  • Let ( u = 2x ) and ( dv = e^x , dx )
  • Then, ( du = 2 , dx ) and ( v = e^x )

  Applying integration by parts again:

  [ \int 2x e^x , dx = 2x e^x - \int e^x (2) , dx ]

  This simplifies to:

  [ \int 2x e^x , dx = 2x e^x - 2e^x ]

  Substituting this back into the original integral:

  [ \int x^2 e^x , dx = x^2 e^x - (2x e^x - 2e^x) ]

  Combining terms, we have:

  [ \int x^2 e^x , dx = x^2 e^x - 2x e^x + 2e^x + C ]

  Thus, the final result for the integral is:

  [ \int x^2 e^x , dx = e^x (x^2 - 2x + 2) + C ]

  Where ( C ) is the constant of integration.

• Test case 2

  Score: 8/10

  Perform the operation of calculating the derivative of x^3 * sin(x) with respect to x.

  1. Check if tool githejie/mcp-server-calculator is needed to perform the task above.

  The task involves calculating the derivative of a mathematical expression. The githejie/mcp-server-calculator tool is designed to evaluate expressions, which includes performing operations like differentiation. Therefore, the tool is needed.

  2. Since a tool is needed, proceed to step 3.

  3. Output "Calling the tool now". Then use the tool githejie/mcp-server-calculator to perform the task.

  Calling the tool now. 4. The tool failed to execute due to an invalid input format. The expression for differentiation should be provided in a more standard mathematical form without the differential operator.

  5. Based on the output of the tool, I will correct the input and perform the calculation again.

  Here is the response to the input task: The derivative of the function ( f(x) = x^3 \sin(x) ) can be calculated using the product rule. According to the product rule:

  [ \frac{d}{dx}(u \cdot v) = u' \cdot v + u \cdot v' ]

  For ( u = x^3 ) and ( v = \sin(x) ):

  • ( u' = 3x^2 )
  • ( v' = \cos(x) )

  Thus, applying the product rule:

  [ f'(x) = 3x^2 \sin(x) + x^3 \cos(x) ]

  So, the derivative of ( x^3 \sin(x) ) with respect to ( x ) is:

  [ f'(x) = 3x^2 \sin(x) + x^3 \cos(x) ]

• Test case 3

  Score: 9/10

  Perform the operation of calculating the limit of (x^2 - 4)/(x - 2) as x approaches 2.

  1. Check if tool githejie/mcp-server-calculator is needed to perform the task above.

  The task involves calculating the limit of a mathematical expression, which can be efficiently handled by the githejie/mcp-server-calculator tool.

  2. Since a tool is needed, proceed to step 3.

  3. Output "Calling the tool now". Then use the tool githejie/mcp-server-calculator to perform the task.

  Calling the tool now. 4. The tool output indicates an error due to an unknown identifier for the limit function.

  Since this seems to be a case of tool malfunction or inability to process the limit calculation directly, I will now proceed to evaluate the limit manually.

  5. Here is the response to the input task:

  To calculate the limit of ((x^2 - 4)/(x - 2)) as (x) approaches 2, we can simplify the expression first:

  1. The expression ((x^2 - 4)) can be factored as ((x - 2)(x + 2)).
  2. Thus, we can rewrite the limit as: [ \lim_{x \to 2} \frac{(x - 2)(x + 2)}{(x - 2)} ]
  3. We can cancel ((x - 2)) from the numerator and denominator (as long as (x \neq 2)): [ \lim_{x \to 2} (x + 2) ]
  4. Now, substituting (x = 2): [ 2 + 2 = 4 ]

  Therefore, the limit of ((x^2 - 4)/(x - 2)) as (x) approaches 2 is (4).

• Test case 4

  Score: 10/10

  Perform the operation of calculating the Taylor series expansion of sin(x) up to the 5th degree term.

  1. Check if tool githejie/mcp-server-calculator is needed to perform the task above.

  The task involves calculating the Taylor series expansion of sin(x) up to the 5th degree term. This is a mathematical operation that can be performed manually or using a calculator tool. Since the task involves a specific calculation, the tool githejie/mcp-server-calculator can be used to perform this task efficiently.

  2. Since a tool is needed, proceed to step 3.

  3. Output "Calling the tool now". Then use the tool githejie/mcp-server-calculator to perform the task.

  Calling the tool now. 4. The tool output indicates that there was an error due to invalid syntax in the expression provided. However, this is likely due to the way the Taylor series was formatted in the input.

  5. Based on the output of the tool, generate a response starting with "Here is the response to the input task: ".

  Here is the response to the input task:

  The Taylor series expansion of sin(x) up to the 5th degree term can be derived as follows:

  [ \sin(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} + O(x^7) ]

  This simplifies to:

  [ \sin(x) \approx x - \frac{x^3}{6} + \frac{x^5}{120} ]

  where (O(x^7)) indicates that the error term is of the order of (x^7) and higher. Thus, the Taylor series expansion of sin(x) up to the 5th degree term is:

  [ \sin(x) \approx x - \frac{x^3}{6} + \frac{x^5}{120} ]