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IBM

MCP Math Server

by IBM

between

Determine if a number falls within a specified range using mathematical interval notation, with exclusive bounds as the default setting.

Instructions

Check if a value is between two bounds (exclusive by default, like mathematical interval notation). (Domain: arithmetic, Category: comparison)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
valueYes
lowerYes
upperYes
Behavior3/5

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

No annotations are provided, so the description carries the full burden. It discloses key behavioral traits: the exclusive default behavior and the mathematical interval notation analogy. However, it lacks details on edge cases (e.g., what happens if lower > upper), return format (e.g., boolean or detailed result), or error handling, leaving some gaps in transparency.

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?

The description is highly concise and well-structured in a single sentence, front-loading the core purpose and efficiently adding domain/category context. Every word contributes value without redundancy, making it easy to parse and understand quickly.

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?

Given the tool's moderate complexity (3 parameters, no output schema, no annotations), the description is adequate but incomplete. It covers the basic purpose and behavior but lacks details on return values, error conditions, or examples. For a comparison tool with numeric inputs, more context on output format or usage scenarios would enhance completeness.

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?

The input schema has 0% description coverage, but the description adds meaningful context by explaining that parameters represent 'value', 'lower', and 'upper' bounds for an interval check. It clarifies the exclusive default behavior, which is not evident from the schema alone. However, it does not detail parameter constraints or interactions, so it partially compensates for the low schema coverage.

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 purpose: 'Check if a value is between two bounds (exclusive by default, like mathematical interval notation).' It specifies the verb ('Check'), resource ('value'), and distinguishes it from siblings by noting its exclusive default behavior and domain/category context, which is unique among the listed sibling tools focused on arithmetic and comparison.

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 provides clear context for when to use this tool by stating its domain ('arithmetic') and category ('comparison'), and implies usage for checking numeric intervals. However, it does not explicitly mention when not to use it or name alternatives (e.g., 'in_range' or 'clamp' from the sibling list), which prevents a perfect score.

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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