CALCULATE_MCP

solve_root

Numerically find the root of an equation within a bracket using bisection. Input an expression, lower and upper bounds, and optional tolerance.

Instructions

Numerically solve f(x)=0 on a bracket using robust bisection.

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "expression": "<expression>",
      "lower": "<lower>",
      "upper": "<upper>"
    },
    "name": "solve_root"
  }
}

Input Schema

Name	Required	Description	Default
`lower`	Yes
`upper`	Yes
`tolerance`	No
`expression`	Yes
`maxIterations`	No

Schema Changelog

Changes observed during successful MCP inspections.

First observedv0.2.0Sep 14, 2026

TDQS

B3/5.0

Behavior3/5

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

With no annotations, the description carries the full behavioral burden. 'Robust bisection' meaningfully signals reliable convergence when the bracket contains a sign change, which is genuine behavioral information, but it omits preconditions (f(lower) and f(upper) must have opposite signs), failure behavior, and convergence/result reporting.

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?

A single front-loaded sentence with a clear verb, objective, and method—zero wasted words.

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?

For a numeric solver with no output schema and five undocumented parameters, one sentence is thin. It doesn't say how the expression is parsed, what the result looks like, or how tolerance/maxIterations affect outcomes, leaving real gaps for correct invocation.

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?

Schema description coverage is 0%, so the description must compensate and it largely does not. 'On a bracket' loosely maps to lower/upper, but expression, tolerance, and maxIterations receive no added meaning beyond their types and defaults in the schema.

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 states a specific verb and resource—'solve f(x)=0'—and adds the algorithmic method ('robust bisection') on a bracket. An agent can immediately tell this is a root-finding tool rather than a general evaluator, though it does not explicitly contrast with siblings like calculate_calculus.

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 phrase 'on a bracket' hints at the precondition of supplying two endpoints, but there is no explicit when-to-use guidance, no mention of when a bracket is required versus other root techniques, and no reference to any alternative sibling tool.

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

Deploy Server