public class Runge2{

    public static double f(double x, double y){
	double f = Math.pow(x,5) * Math.pow(Math.E,Math.pow(x,3));
	return f;
    }

    /* This is the Runge Function given in class */

    public static double rk(double x, double y, double step){
	double h = step;
	double k1 = h * f(x, y);
	double k2 = h * f(x + h/2, y + k1/2);
	double k3 = h * f(x + h/2, y + k2/2);
	double k4 = h * f(x + h, y + k3);

	return y += k1/6 + k2/3+ k3/3 + k4/6;
    }

    public static void main(String[] args){



	try{

	double stepSize = Double.parseDouble(args[0]);


	/* this sets the range of the integral */

	double initial = 0;
      	double end = 1;

	/* steps is total steps and finalY is the value of the integral */

        double steps = (end - initial) / stepSize;
	double i = 0;
	double finalY = 0;

	if (stepSize <= 0)
	    throw new Exception("Error: Stepsize is negative or 0. \n");

	for (i = 0; i < steps ; i++){
	    finalY += rk(initial + i * stepSize,
			 0, stepSize);
	}

	System.out.printf("The Runge Kutta method gives the value \n" );
	System.out.printf("%1.4f as the integral of x^5 * e^x^3  \n",
			  finalY);
	System.out.printf("on the interval of %1.4f to %1.4f  \n",
			  initial, end );
	System.out.printf("using %1.0f steps and a step size of %1.6f \n",
			  steps,stepSize);

        if (stepSize > 1.0)
	    throw new Exception("Warning: Stepsize is large. Values may be off.\n");
	}

	catch(Exception e){
    	    System.out.printf(e.getMessage());
    	    System.out.printf("\nYou need to input a float point value \n");
	    System.out.printf("For the value of the step size. To get a \n");
	    System.out.printf("reasonable answer, this step size should \n");
	    System.out.printf("be fairly small, non-negative and entered \n");
	    System.out.printf("as a command line argument, thank you. \n");

    	}


    }
}