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mathmethods-mcp

mathmethods-mcp

by agmonetti
OverviewSchemaSourceRelated ServersDiscussionsAdmin
Python
Hybrid

mc_valor_promedio_1d

Estimate a definite integral with the mean-value Monte Carlo method and return the result, confidence interval, and sample statistics.

Instructions

Estimate ∫ₐᵇ f(x) dx with the mean-value Monte Carlo method.

Args: func_str: Math expression in x. a, b: Integration limits (b > a). N: Number of samples. seed: Optional RNG seed for reproducibility. precision: Rounding digits. nivel_confianza: Confidence level in (0, 1). plot: When True, also return a PNG scatter plot of the samples.

Returns: Dict with the estimate, confidence interval and sample statistics. With plot=True a list [dict, Image] is returned instead.

Input Schema

NameRequiredDescriptionDefault
NNo
aYes
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

A3.5/5.0
Behavior3/5

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

With no annotations, the description carries the full burden and does disclose the return contract: a dict with estimate, confidence interval and sample statistics, or [dict, Image] when plot=True. It does not mention accuracy characteristics of the Monte Carlo estimator, cost relative to N, or error behavior beyond the b > a note.

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?

Purpose sentence first, then a compact Args block, then Returns — no filler and no repetition. Each line earns its place given the 0% schema coverage.

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?

With no annotations and no output schema, the description adequately compensates by documenting all parameters and the return shape, including the plot=True variant. It omits defaults (N, precision, nivel_confianza) and any guidance on selecting N, but nothing essential for a correct call is missing.

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 there are 8 parameters, so the arg list is the only documentation. It covers every parameter and adds meaning beyond the schema: seed exists for reproducibility, precision controls rounding digits, nivel_confianza is bounded to (0,1), and plot changes the return shape rather than just toggling a flag.

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?

The description opens with a specific verb and resource ('Estimate ∫ₐᵇ f(x) dx') and names the algorithm ('mean-value Monte Carlo method'), which implicitly separates it from siblings like mc_hit_or_miss_1d or integral_simpson13. It never explicitly names an alternative, but the method specificity is enough to identify the tool.

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 statement of when to choose this estimator over mc_hit_or_miss_1d, mc_estadistico_1d, or the deterministic quadrature siblings. The only constraint offered is b > a, which is a validity rule rather than usage guidance.

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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