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IBM

MCP Math Server

by IBM

nth_power_of_two

Calculate 2 raised to any integer power n to compute exponential values for mathematical sequences and binary operations.

Instructions

Get the nth power of two (0-indexed). (Domain: arithmetic, Category: basic_sequences)

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 the full burden of behavioral disclosure. It states the tool 'Get[s] the nth power of two,' implying a read-only operation, but does not address potential errors (e.g., negative or large 'n' values), performance characteristics, or output format. For a tool with no annotations, this leaves significant behavioral gaps, though it at least implies a safe read operation.

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 front-loaded: a single sentence that directly states the tool's purpose with no wasted words. The additional domain and category information is brief and relevant, making it efficient and easy to parse.

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 integer parameter) and lack of annotations or output schema, the description is minimally adequate. It covers the basic purpose and parameter semantics but lacks details on usage guidelines, behavioral traits, and error handling. For such a simple tool, it meets the minimum viable threshold but has clear gaps in 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 one parameter 'n' with 0% description coverage, so the description must compensate. It adds that 'n' is '0-indexed,' which clarifies the indexing semantics beyond the schema's type ('integer'). However, it does not explain valid ranges, constraints, or examples, leaving some ambiguity. Given the low schema coverage, this partial compensation justifies a baseline score.

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?

The description clearly states the tool's purpose: 'Get the nth power of two (0-indexed).' It specifies the verb ('Get'), resource ('nth power of two'), and clarifies indexing ('0-indexed'), which is helpful. However, it does not explicitly differentiate from sibling tools like 'powers_of_two' or 'is_power_of_two', which are related but distinct operations, so it falls short of a perfect score.

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 guidance on when to use this tool versus alternatives. It mentions a domain ('arithmetic') and category ('basic_sequences'), but this is too vague to inform usage decisions. There is no mention of prerequisites, constraints, or comparison to sibling tools like 'powers_of_two' or 'is_power_of_two', leaving the agent without clear direction.

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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