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mathmethods-mcp

mathmethods-mcp

integral_simpson38

Approximate definite integrals using the composite Simpson 3/8 rule. Provide function, limits, and number of subintervals to get integral, error estimates, and optional plot.

Instructions

Approximate ∫ₐᵇ f(x) dx with the composite Simpson 3/8 rule.

Args: func_str: Math expression in x. a, b: Integration limits (b > a). n: Number of subintervals (must be a multiple of 3). epsilon: Optional point in [a, b] for the truncation error bound. precision: Rounding digits. plot: When True, also return a PNG plot of f(x) over [a, b].

Returns: Dict with the integral, error estimates and table. With plot=True a list [dict, Image] is returned instead.

Input Schema

NameRequiredDescriptionDefault
aYes
bYes
nYes
plotNo
epsilonNo
func_strYes
precisionNo

Schema Changelog

Changes observed during successful MCP inspections.

  1. Changed1 schema field changedv0.2.1
    • addedInput schema / properties / plot
      Added value: +{
      +  "default": false,
      +  "title": "Plot",
      +  "type": "boolean"
      +}
  2. First observedv0.1.0

TDQS

A3.6/5.0
Behavior4/5

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

With no annotations, the description carries the full burden and does a solid job: it discloses the return type (dict with integral, error estimates and table) and the conditional return shape (list [dict, Image] when plot=True), plus input constraints (b > a, n multiple of 3). It doesn't cover error/failure behavior, but for a pure read-only math function that is minor.

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?

Content is front-loaded with a clear one-line purpose, followed by structured Args and Returns sections. Slightly docstring-formatted rather than prose, but every line carries information with no filler.

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?

Given no output schema and no annotations, the description supplies both the parameter semantics and the return structure the agent needs. It is nearly complete for a 7-parameter numeric tool; only failure/edge-case behavior (e.g., invalid expressions) is unaddressed.

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

Parameters4/5

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

Schema description coverage is 0% and all 7 parameters are undocumented in the schema, so the description must compensate. It explains every parameter meaningfully: func_str as an expression in x, a/b as limits with b > a, n as a multiple of 3, epsilon as an optional error-bound point, precision as rounding digits, and plot's effect. Only default values and accepted expression syntax are left implicit.

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 precise verb and resource ('Approximate ∫ₐᵇ f(x) dx with the composite Simpson 3/8 rule'), which tells the agent exactly which method is applied. The named rule implicitly distinguishes it from the sibling integral_simpson13 and integral_trapecio, though it never explicitly contrasts them.

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?

The description gives the mathematical operation but no when-to-use guidance relative to the many sibling integrators (simpson13, trapecio, rectangulo, comparar). The only constraint offered is that n must be a multiple of 3, which is a correctness rule, not usage guidance.

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