Skip to main content
Glama
IBM

MCP Math Server

by IBM

integrate_midpoint

Calculate definite integrals using the midpoint rule for numerical approximation of area under a curve. Provide function, interval bounds, and optional step count.

Instructions

Calculate definite integral using the midpoint rule (Domain: calculus, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
funcYes
aYes
bYes
n_stepsNo
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 calculates a definite integral but does not describe key behaviors such as error handling, performance characteristics, or what the output looks like (e.g., numeric result, error estimate). For a computational tool with zero annotation coverage, this is a significant gap 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.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is concise and front-loaded, stating the core purpose in a single sentence. It avoids unnecessary words, but the inclusion of 'Domain: calculus, Category: general' adds minimal value and could be considered slightly redundant. Overall, it is efficiently structured with no wasted sentences.

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?

Given the complexity of a numerical integration tool with 4 parameters, 0% schema coverage, no annotations, and no output schema, the description is incomplete. It fails to explain parameter meanings, expected output format, error behavior, or usage context. This leaves the agent with insufficient information to use the tool effectively.

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%, meaning none of the parameters (func, a, b, n_steps) are documented in the schema. The description does not add any semantic information about these parameters—it does not explain what 'func' should contain (e.g., a mathematical expression), what 'a' and 'b' represent (integration limits), or the role of 'n_steps' (number of subdivisions). This leaves all parameters unexplained.

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: 'Calculate definite integral using the midpoint rule'. It specifies the verb ('calculate'), resource ('definite integral'), and method ('midpoint rule'), which is specific and unambiguous. However, it does not explicitly differentiate from sibling tools like 'integrate_simpson' or 'integrate_trapezoid', which are also numerical integration methods, so it misses full sibling distinction.

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 the domain ('calculus') and category ('general'), but this is too vague to inform usage decisions. There is no mention of when this method is preferred over other integration tools or any prerequisites, leaving the agent without practical usage instructions.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

Install Server

Other Tools

Latest Blog Posts

MCP directory API

We provide all the information about MCP servers via our MCP API.

curl -X GET 'https://glama.ai/api/mcp/v1/servers/IBM/chuk-mcp-math-server'

If you have feedback or need assistance with the MCP directory API, please join our Discord server