coding UTF-8;         // Specify character encoding (to avoid text corruption)
import Math;          // Import math function library
import tool.Graph2D;  // Import graphing library


// Parameter constants for integration
const double A = 0.0;  // Lower bound of integration interval
const double B = 1.0;  // Upper bound of integration interval
const int N = 10;      // Number of small intervals (larger = finer = more accurate)

// The function to be integrated: f(x) = cos(x)
double f(double x) {
	return cos(x);
}

// ---------------------------------------------
// Numerical integration using Simpson's Rule
// ---------------------------------------------

double delta = (B - A) / N;  // Width of a small interval (Delta x)
double value = 0.0;          // Result of integration (total area)

for(int i=0; i<N; i++) {
	
	// X-coordinate of the left edge of the i-th interval
	double x = A + i * delta;
	
	// Output the current integration result up to x
	println(x, value); // (Comment out this line for large N to improve speed)
	
	// Add the area of the i-th interval to the total
	value += ( f(x) + f(x+delta) + 4.0 * f(x+delta/2.0) ) * delta / 6.0;
}

// Output the final result of the integration
println(B, value);

// Plot the output data to a graph
// (Comment out this line for large N to avoid slowdown)
setGraph2DData(newGraph2D(), load());