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Glama
agmonetti

mathmethods-mcp

mc_valor_promedio_2d

Estimate a double integral over a rectangular region using mean-value Monte Carlo sampling, with an optional scatter plot of sampled points colored by function value.

Instructions

Estimate the double integral of f(x, y) over [x_a,x_b]×[y_a,y_b] by mean value.

With plot=True a PNG scatter of the sampled points coloured by f(x, y) is returned as [dict, Image] alongside the numeric result.

Input Schema

NameRequiredDescriptionDefault
NNo
x_aYes
x_bYes
y_aYes
y_bYes
plotNo
seedNo
func_strYes
precisionNo
nivel_confianzaNo

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

C2.9/5.0
Behavior3/5

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

With no annotations the description carries the full burden. It usefully discloses that plot=True changes the return to [dict, Image] with a coloured scatter, which is real behavioral information beyond the schema. However, it omits that this is a stochastic estimator whose result is approximate, and says nothing about the statistical machinery implied by N, seed, precision and nivel_confianza.

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?

Two short sentences, front-loaded with the core operation and followed by the conditional return behavior. Little waste, though the mechanism it uses (mean value) is asserted rather than made actionable.

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 10-parameter stochastic tool with no annotations and no output schema, the description is thin. It leaves the sampling parameters, the confidence/precision behavior, and the approximate nature of the result undocumented, so an agent cannot call it correctly or interpret the output on the description alone.

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 description coverage is 0%, so the description must compensate, and it only partially does. It implies the meaning of func_str and the four bounds through notation and explains plot, but N (sample count), seed (reproducibility), precision and nivel_confianza (confidence level) go entirely unexplained.

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 ("Estimate") and resource (the double integral of f(x,y) over a rectangle) and pins the method ("by mean value"). The mention of a 2D domain and mean-value estimator distinguishes it from hit-or-miss and from the 1d/3d variants, though it never names an alternative explicitly.

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?

There is no when-to-use or when-not guidance. Nothing tells the agent when mean-value Monte Carlo is preferable to the deterministic siblings like integral_simpson13 or integral_trapecio, nor when to choose this over mc_hit_or_miss_1d. Usage is only implied by the method name.

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