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mAd-DaWg

mcp_calculator

by mAd-DaWg

fmax

Approximate the maximum value of a mathematical function f(x) over a closed interval by providing the expression and bounds.

Instructions

When: approximate maximum of infix f(x) on a closed interval. Params: expression in x; lower; upper; angle_mode; tol. Example: expression="-(x-1)^2", lower=0, upper=2.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
tolNo
lowerYes
upperYes
angle_modeNorad
expressionYes

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes
Behavior3/5

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

With no annotations provided, the description carries the responsibility for behavioral disclosure. It mentions 'approximate', indicating a numerical method, and the 'closed interval' constraint. However, it does not explain behavior for multiple local maxima, error handling, or the effects of the `angle_mode` and `tol` parameters. The description is adequate but not deeply transparent.

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 very brief (three short sentences) and structured with 'When:', 'Params:', and 'Example:'. It front-loads the purpose and includes a concrete example that aids understanding. The 'Params:' list is skeletal but readable. No wasted words, though slightly choppy.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness3/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

An output schema exists, so return values are covered. However, the description omits details about `angle_mode` and `tol`, does not mention edge cases or limitations, and does not reference sibling tools. It provides a working example but is not fully self-sufficient for an agent unfamiliar with the tool.

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?

The schema description coverage is 0%, so the description must compensate. It lists parameters and clarifies 'expression in x', and the 'closed interval' gives implied meaning to `lower` and `upper`. However, `angle_mode` and `tol` are unexplained, and the example only uses three required parameters. This is a significant gap for a 5-parameter tool.

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 explicitly states 'approximate maximum of infix f(x) on a closed interval', providing a specific verb ('approximate'), resource ('f(x)'), and scope ('closed interval'). This clearly distinguishes it from sibling tools like fmin (minimum) and other math operations.

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 starts with 'When:' and clearly states the use case for finding an approximate maximum on a closed interval. It does not explicitly mention alternatives or when not to use, but the context is sufficient for an agent to decide. It lacks exclusions but provides a clear 'when to use'.

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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