MCP Calc Tools

Instructions

Implementation Reference

• index.js:143-145 (handler)

  Handler function for the 'area' tool. It invokes the riemannSum helper with the trapezoid method to approximate the area under the curve (definite integral).

  async ({ expression, start, end, n = 1000 }) => {
    return riemannSum(expression, 'x', start, end, n, 'trapezoid');
  }

• index.js:135-141 (schema)

  Input and output schema for the 'area' tool. Defines parameters: expression (string), start/end (numbers), optional n (subintervals). Outputs a number.

  inputSchema: z.object({
    expression: z.string(),
    start: z.number(),
    end: z.number(),
    n: z.number().optional().describe('Number of subintervals (default: 1000)')
  }),
  outputSchema: z.number(),

• index.js:131-146 (registration)

  Registration of the 'area' tool via ai.defineTool, including name, description, schema, and inline handler.

  ai.defineTool(
    {
      name: 'area',
      description: 'Calculate the area under a curve between two points',
      inputSchema: z.object({
        expression: z.string(),
        start: z.number(),
        end: z.number(),
        n: z.number().optional().describe('Number of subintervals (default: 1000)')
      }),
      outputSchema: z.number(),
    },
    async ({ expression, start, end, n = 1000 }) => {
      return riemannSum(expression, 'x', start, end, n, 'trapezoid');
    }
  );

• index.js:43-76 (helper)

  riemannSum helper function that performs numerical integration using left, right, midpoint, or trapezoid Riemann sums. Used by the 'area' handler with 'trapezoid' method.

  const riemannSum = (expr, variable, a, b, n, method = 'midpoint') => {
    try {
      const deltaX = (b - a) / n;
      let sum = 0;
      const node = math.parse(expr);
      const scope = {};
      
      if (method === 'left' || method === 'right') {
        const offset = method === 'right' ? 1 : 0;
        for (let i = 0; i < n; i++) {
          const x = a + (i + offset) * deltaX;
          scope[variable] = x;
          sum += math.evaluate(node, scope) * deltaX;
        }
      } else if (method === 'midpoint') {
        for (let i = 0; i < n; i++) {
          const x = a + (i + 0.5) * deltaX;
          scope[variable] = x;
          sum += math.evaluate(node, scope) * deltaX;
        }
      } else if (method === 'trapezoid') {
        for (let i = 0; i <= n; i++) {
          const x = a + i * deltaX;
          scope[variable] = x;
          const coef = (i === 0 || i === n) ? 0.5 : 1;
          sum += coef * math.evaluate(node, scope) * deltaX;
        }
      }
      
      return sum;
    } catch (e) {
      return `Error: ${e.message}`;
    }
  };