Evaluate the definite integral of an expression over a given interval, with support for infinite and pi bounds.
Definite integral of expression from lower to upper.
Bounds are expressions, so oo / -oo / pi are accepted.
| Name | Required | Description | Default |
|---|---|---|---|
| lower | No | 0 | |
| upper | No | 1 | |
| variable | No | x | |
| expression | Yes |
| Name | Required | Description | Default |
|---|---|---|---|
| result | Yes |
Changes observed during successful MCP inspections.
v0.3.0Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries the full burden. It adds one useful behavioral trait: bounds accept symbolic expressions like `oo`, `-oo`, and `pi`. However, it omits other behavioral details such as error handling, required permissions, or the role of the `variable` parameter.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is two short sentences, front-loaded with the core operation and followed by a useful note. Every sentence earns its place with no wasted words.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
An output schema exists, so return values need not be explained. However, with 0% schema description coverage and no annotations, the description leaves critical gaps: the `variable` parameter is unmentioned, and there is no usage guidance or error behavior. For a tool with four parameters, this is insufficient.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 0%, so the description must compensate. It names expression, lower, and upper, and explains that bounds are expressions, but it completely ignores the `variable` parameter. It also provides no syntax guidance for the `expression` parameter itself.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the operation ('Definite integral') and the resources (expression, lower, upper), distinguishing it from the indefinite sibling 'integrate' by name. However, it does not explicitly mention that sibling or contrast the tools, so it falls short of a 5.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
No when-to-use guidance is provided. The description does not indicate when to choose this tool over alternatives like `integrate`, nor does it mention any prerequisites or conditions. Usage is only implied by the name.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.