Major problems I see is you are struggling with the syntax and logic. We will focus one at a time. If you are comfortable in python write the code in python ( less worry about syntax) and then I will help you write cpp or you can figure out on your own.

Revise last lab, We have covered recursion, loops and lab before that we covered input output, datatypes and precision. In this lab we will learn about functions.

Lets get back to our initial problem. We will start with simple functions.

The solution of the problem is given below.

#include <iostream>
#include <math.h>
#include <iomanip>

// YOUR FUNCTIONS GO HERE
double Fn(double x){
  return -6*pow(x,2) +5*x +3;
}
double Integral(double x){
  return -2*pow(x,3) +5*pow(x,2)/2 +3*x;
}

double EstimateWithTraps(double a, double b, int n){
  double dx = (b - a)/n;
  double area_dx =0;
  double x =a;
  for(int i=0;i<n;i++){
    area_dx += dx*(std::abs(Fn(x)) + std::abs(Fn(x+dx)))/2;
    x +=dx;
  }
  return area_dx;
}

// Trapezoid calculation method...
int main()
{
  double a,b,tolerance,estimated_area,actual_area,curr_tolerance;
  int n;
  std::cout <<  "Lower Range:" << std::endl;
  std::cin >>  a;
  std::cout << "Upper Range:" << std::endl;
  std::cin >>  b;
  std::cout << "Tolerance:" << std::endl;
  std::cin >>  tolerance;
  std::cout << "Initial trapezoid count:" << std::endl;
  std::cin >>  n;
  curr_tolerance = tolerance +1;
  while(curr_tolerance>tolerance){
    estimated_area = EstimateWithTraps(a,b,n);
    actual_area = std::abs(Integral(b)) - std::abs(Integral(a));
    curr_tolerance = std::abs(estimated_area- actual_area);
    std::cout <<  "Estimate:"<<  std::fixed <<  std::setprecision(4) << estimated_area <<  ", Number of Traps:"<< n<< ", Diff:"<< curr_tolerance<< std::endl;
    n = n*2;
  }
  return 0;

}