//File1.c        //Compliant
// r = power(x,n) returns the nth power of x into y
// r is long long
// x is double
// n must be integer
 long long power(double x, int n){
	 long long BN = 1;
	 for(int i = 0; i<n;++i){
		 BN*=x;
	 }
	 return BN;
 }
 // n = AppxIndex(m,f) calculates the approximate
//  effective index of a material
// n is a double, represent the effective index of a mixture
// m is a double, represents the relative index of the 
//                  inclusion compared to the background material
// f is a double, represents the filling factor of the inclusion
// The function implements the formula in the doi 10.XXYY 
 double AppxIndex(double m, double f){
	 // This function implements the formula for approximate index
	 // The first term is U:
	 double U = (power(m,2) - 1)/(power(m,2)+2);
	 //The second term is V:
	 double V = (power(m,4) + 27*power(m,2)+38)/(2*power(m,2)+3);
	 // Calculate the denominator
	 double den = ( (1-2*f*power(U,2)*
              (1+power(m,2)*U*V + power(m,3)/power(m,3)*(U-V))));
	 // Calculate the numerator
	 double num = (1+2*f*power(U,2)
              *(1+power(m,2)*U*V + power(m,3)/power(m,3)*(U-V)));
	 // Calculate the aproximate index
	 // Return by value
	 return num/den;
 }