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IBM

MCP Math Server

by IBM

square_numbers

Generate the first n square numbers (1, 4, 9, 16, 25, ...) using the formula n². This tool calculates square numbers for arithmetic and mathematical computations.

Instructions

Generate the first n square numbers (1, 4, 9, 16, 25, ...). nth square number = n². (Domain: arithmetic, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes
Behavior2/5

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

No annotations are provided, so the description carries full burden. It states what the tool does (generates square numbers) but lacks behavioral details such as: what happens if n is negative or zero, whether there are limits on n, the format of the output (list, array, string), or error handling. The description provides basic functionality but misses important operational context needed for reliable use.

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 extremely concise and front-loaded: the first sentence states the core purpose, the second provides the mathematical rule, and the third adds domain context. Every sentence earns its place with no wasted words, making it easy to parse quickly while remaining informative.

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 low complexity (one parameter, simple arithmetic function) but lack of annotations and output schema, the description is minimally complete. It explains what the tool does and the parameter's role, but fails to describe output format, edge cases, or error behavior. For a tool with no structured output documentation, this leaves significant gaps in usability despite adequate basic coverage.

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 description coverage is 0%, so the description must compensate. It adds meaning by explaining that parameter 'n' determines 'the first n square numbers' and provides the formula 'n²', clarifying the mathematical relationship. However, it does not specify constraints (e.g., n must be positive integer) or examples beyond the sequence snippet, leaving some semantic gaps despite adding value over the bare schema.

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 specific verb ('Generate') and resource ('first n square numbers'), with a precise mathematical definition ('nth square number = n²') and example sequence. It explicitly distinguishes this tool from sibling tools like 'cube_numbers', 'nth_perfect_square', and 'perfect_squares' by focusing on generating a sequence of squares rather than testing or retrieving individual squares.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description implies usage through the mathematical context ('Domain: arithmetic, Category: general'), but does not explicitly state when to use this tool versus alternatives like 'nth_perfect_square' (which returns a single square) or 'perfect_squares' (which might list squares up to a limit). No explicit when-not or alternative guidance is provided, leaving usage contextually implied rather than clearly defined.

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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