Mathematical Calculator MCP Server

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plot_function

Plots y = f(x) from a mathematical expression over a specified x range and sample count, returning a PNG graph for visual analysis.

Instructions

Plots a graph of y = f(x).

Args: expression: The function expression as a string. start: The first x value to plot. end: The final x value to plot. step: The number of x samples to render.

Returns: On success: {"result": "Plot generated successfully.", "format": "png", ...} On error: {"error": }

Notes: - Use 'x' as the variable (e.g., x2, not x^2) - Multiplication must be explicitly indicated with * (e.g., 2*x, not 2x) - Powers can be represented with ** or ^ (e.g., x2 or x^2)

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": {
      "expression": "<expression>"
    },
    "name": "plot_function"
  }
}

Input Schema

Name	Required	Description	Default
`end`	No
`step`	No
`start`	No
`expression`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedv1.1.1Oct 20, 2026

TDQS

A3.8/5.0

Behavior4/5

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

With no annotations provided, the description carries the full burden and largely does so: it discloses the success payload shape ({result, format: png}), the error payload shape, and expression-syntax rules. It does not disclose limits (e.g., discontinuity handling, valid ranges, or failure conditions for malformed expressions), which keeps it from a 5.

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?

Front-loads the purpose in one sentence, then organizes Args/Returns/Notes cleanly. The Notes on variable naming and multiplication are useful rather than filler, though the section structure adds slight verbosity.

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

Completeness4/5

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

No output schema exists, but the description supplies return and error shapes, and the notes cover expression syntax pitfalls. Complete enough to invoke correctly; only edge-case behavior (invalid domains, sampling limits) is unaddressed.

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

Parameters5/5

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

Schema description coverage is 0%, so the description must compensate — and it does, defining each of the four parameters. Notably it clarifies that 'step' means the number of x samples to render rather than a step size, resolving a genuine naming ambiguity that the schema alone would not.

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?

States a specific verb and resource ('Plots a graph of y = f(x)'), which is clear and unambiguous. It does not explicitly distinguish itself from plotting-adjacent siblings like solve_equation, differentiate, or integrate, but the operation is distinct enough that an agent can route correctly.

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 versus alternatives such as solve_equation or calculate, and no prerequisites or limitations stated. Usage is only implied by the argument list, which is insufficient for a math-plotting tool amid many numeric siblings.

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