CALCULATE_MCP

calculate_calculus

Compute numerical derivative or definite integral for one-variable expressions using five-point method or Simpson's rule.

Instructions

Numerical calculus for one-variable expressions: five-point numerical derivative or Simpson definite integral.

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "operation": "<operation>",
      "expression": "<expression>"
    },
    "name": "calculate_calculus"
  }
}

Input Schema

Name	Required	Description	Default
`x`	No
`step`	No
`lower`	No
`upper`	No
`intervals`	No
`operation`	Yes
`expression`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedv0.2.0Sep 14, 2026

TDQS

C2.7/5.0

Behavior2/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations, the description carries the full burden, and it only discloses the numerical methods used. It says nothing about accuracy/precision limits, how step or intervals affect results, failure modes for invalid expressions, or return format.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

A single dense sentence that front-loads the domain and enumerates the two operations with their algorithms. No waste, though it is arguably too terse given the undocumented parameters.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness2/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a 7-parameter numerical tool with no annotations and no output schema, the description is too thin. It leaves the agent without guidance on required inputs beyond operation/expression or on interpreting results.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters2/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 0% for 7 parameters, and the description only obliquely maps 'one-variable expressions' to x and names the two operations. Parameters step, lower, upper, and intervals are completely undocumented anywhere, which is a significant gap for a numerical method whose accuracy depends on them.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

Names the resource (one-variable calculus) and the specific operations (five-point numerical derivative, Simpson definite integral), which is more precise than the generic siblings like calculate_expression. It does not explicitly differentiate itself from calculate_expression or solve_root, so it stops short of a 5.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

No guidance on when to use this tool versus calculate_expression, solve_root, or calculate_matrix. The choice between derivative and integral is left entirely to the operation enum in the schema rather than being framed in prose.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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