Skip to main content
Glama
mathmethods-mcp

mathmethods-mcp

integral_comparar

Compares rectangle, trapezoid, Simpson 1/3, and Simpson 3/8 rules on the same integral, returning per-method results and an optional bar chart.

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. Must be a multiple of 6 (2 for Simpson 1/3 and 3 for Simpson 3/8), so all four rules can run on the same grid. epsilon, precision: Error-bound and rounding settings. plot: When True, also return a PNG bar chart comparing the four rules.

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

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 burden and does disclose the return structure: a dict with per-method results and success flags, or [dict, Image] when plot=True. It also states the n-multiple-of-6 constraint, though it does not describe error behavior beyond the mentioned success flags.

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 front-loaded with the core comparison purpose, then uses a compact Args/Returns structure with no wasted sentences. Each listed parameter adds necessary constraint or format information.

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, so the description appropriately explains the return dict and plot variant. It covers required inputs and constraints well enough to invoke correctly; remaining gaps are minor, such as exact failure modes or exception behavior.

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: func_str is a math expression in x, a and b are integration limits with b > a, n is subinterval count with a multiple-of-6 constraint, epsilon/precision are error-bound and rounding settings, and plot triggers a PNG bar chart. All seven parameters are addressed with meaning beyond their titles.

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?

States a specific verb (compare) and resource (rectangle, trapezoid, Simpson 1/3, Simpson 3/8 on the same integral). It clearly distinguishes the tool from siblings such as integral_simpson13 or integral_trapecio, which compute one rule at a time.

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 makes clear this tool is for comparing all four integration rules at once and gives the key usage constraint that n must be a multiple of 6 so all rules share a grid. It does not explicitly name when to prefer this over individual sibling tools, but the comparison context is unambiguous.

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