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agmonetti

mathmethods-mcp

by agmonetti

integral_comparar

Compare rectangle, trapezoid, Simpson 1/3, and Simpson 3/8 on the same integral, returning per-method results and success flags.

Instructions

Compare rectangle, trapezoid, Simpson 1/3 and Simpson 3/8 on the same integral.

Args: func_str: Math expression in x. a, b: Integration limits (b > a). n: Number of subintervals (Simpson 1/3 needs even, 3/8 needs multiple of 3). epsilon, precision: Error-bound and rounding settings.

Returns: Dict with per-method results and success flags.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
aYes
bYes
nYes
epsilonNo
func_strYes
precisionNo
Install Server

TDQS

A4.5/5.0
Behavior4/5

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

With no annotations, the description carries the weight of behavioral disclosure. It reveals that the tool returns a dict with per-method results and success flags, and that n has method-specific divisibility requirements. This adds meaningful behavioral context beyond a simple 'compare' statement, though it does not detail error handling or edge cases.

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

Conciseness5/5

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

The description is efficiently structured: a one-sentence summary frontloads the purpose, followed by a concise docstring. Every sentence provides necessary information (parameters, returns) and there is no verbosity or repetition of schema fields.

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?

For a tool with no output schema and 4 required parameters, the description covers the essential aspects: purpose, parameter constraints, and return type. It does not describe the exact structure of the result dict beyond success flags, but for a numerical comparison tool the provided detail is largely sufficient for an agent to select and invoke it correctly.

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 fully compensates. The docstring explains each parameter's role: func_str is a math expression in x, a and b are limits with b > a, n is the number of subintervals with specific constraints for Simpson methods, and epsilon/precision are error-bound and rounding settings. This adds substantial meaning beyond the schema's bare type definitions.

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

Purpose5/5

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

The description clearly states the tool's purpose: compare rectangle, trapezoid, Simpson 1/3 and Simpson 3/8 on the same integral. This uses a specific verb ('compare') and resource (integral methods), and distinguishes it from sibling tools that implement individual methods (integral_simpson13, integral_simpson38, integral_trapecio, integral_rectangulo).

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

Usage Guidelines4/5

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

The description conveys clear context: it is for comparing numerical integration methods on the same integral. It does not explicitly state when not to use this tool or mention alternatives directly, but the title and sibling names make the comparison context unambiguous. The constraints on n (even for Simpson 1/3, multiple of 3 for Simpson 3/8) provide implicit guidance on valid usage.

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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