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agmonetti

mathmethods-mcp

by agmonetti

mc_valor_promedio_3d

Compute the triple integral of a function f(x,y,z) over a specified rectangular box using Monte Carlo sampling, returning the estimated value with a confidence level.

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].

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
NNo
x_aYes
x_bYes
y_aYes
y_bYes
z_aYes
z_bYes
seedNo
func_strYes
precisionNo
nivel_confianzaNo
Install Server

TDQS

C2.9/5.0
Behavior2/5

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

No annotations are present, so the description carries full responsibility for behavioral disclosure. It merely says 'Estimate' but does not reveal that this is a Monte Carlo method with stochastic output, that results depend on N and seed, or that confidence level and precision are configurable. This is a significant transparency gap for a probabilistic tool.

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?

The description is a single, front-loaded sentence with no redundant words, which makes it easy to parse. However, given the tool's complexity (11 parameters, Monte Carlo behavior, confidence levels), the brevity borders on under-specification, so it earns a 4 rather than a 5.

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?

The tool has a rich parameter set and no output schema, yet the description offers no details about return values, error behavior, stochastic convergence, or how to specify the function. This leaves the agent unprepared to interpret results or configure the method confidently.

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?

With 0% schema description coverage, the description must compensate, but it only adds meaning for the integration bounds (x_a, x_b, etc.) and the function func_str. The crucial parameters N, seed, precision, and nivel_confianza are left undocumented in both the schema and the description, so the agent lacks essential meaning for configuring the Monte Carlo process.

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 action ('Estimate the triple integral'), specifies the target function f(x,y,z), and defines the integration domain as a box with bounds [x_a,x_b]×[y_a,y_b]×[z_a,z_b]. This distinctively separates it from Monte Carlo variants for 1D/2D integrals and deterministic integration tools.

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?

The description provides no explicit guidance on when to use this tool versus alternatives. It only implies suitability for triple integrals over a rectangular box, with no mention of preferred scenarios, limitations, or exclusions relative to sibling tools like mc_valor_promedio_2d or integral_simpson38.

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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