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double trapezoidalIntegral(double a, double b, int n, const std::function<double (double)> &f) {
const double width = (b-a)/n;
double trapezoidal_integral = 0;
for(int step = 0; step < n; step++) {
const double x1 = a + step*width;
const double x2 = a + (step+1)*width;
trapezoidal_integral += 0.5*(x2-x1)*(f(x1) + f(x2));
return trapezoidal_integral;
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