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mathmethods-mcp

mathmethods-mcp

by agmonetti
OverviewSchemaSourceRelated ServersDiscussionsAdmin
Python
Hybrid

mc_valor_promedio_3d

Estimate triple integrals of f(x,y,z) over a rectangular 3D box via Monte Carlo sampling, with an optional PNG histogram of sampled values.

Instructions

Estimate the triple integral of f(x,y,z) over the box [x_a,x_b]×[y_a,y_b]×[z_a,z_b].

With plot=True a PNG histogram of the sampled f values is returned as [dict, Image] alongside the numeric result.

Input Schema

NameRequiredDescriptionDefault
NNo
x_aYes
x_bYes
y_aYes
y_bYes
z_aYes
z_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

B3.1/5.0
Behavior3/5

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

No annotations exist, so the description carries the full burden. It does disclose a genuinely non-obvious behavioral trait: plot=True changes the return type to [dict, Image] with a PNG histogram. However it omits key traits of a Monte-Carlo estimator such as the statistical nature of the result and how N/seed affect reproducibility.

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 tight sentences with the core purpose front-loaded and the return-format caveat second. No filler; the plot note earns its place by describing an observable output change.

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?

With 12 parameters, no annotations, and no output schema, the description should do more. It leaves the confidence-level and precision parameters undefined, so an agent cannot reason about the accuracy contract of the estimate or reproduce a run.

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

Parameters3/5

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

Schema coverage is 0%, so the description must carry semantics. The [x_a,x_b]×[y_a,y_b]×[z_a,z_b] notation grounds six of the parameters and 'plot=True' explains a seventh, but N, seed, precision, and nivel_confianza (the most non-obvious, MC-specific params) are left 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 ('triple integral of f(x,y,z)') with the integration domain spelled out as a box. The 3D/dimensional framing implicitly distinguishes it from the mc_valor_promedio_1d/2d siblings, though it does not name 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?

No when-to-use guidance and no routing to alternatives. Given many sibling integral methods (integral_simpson13, mc_hit_or_miss_1d, mc_valor_promedio_2d), the agent gets no signal on when Monte-Carlo averaging beats a deterministic rule or another MC variant.

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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