Edit: Fixed it :) Thanks for the response. I'm using Bamtools API for C++ (and learning C++). Here's my code

#include "api/BamMultiReader.h"
#include "api/BamWriter.h"
#include <string>
#include <vector>
#include <iostream>
#include <numeric>
using namespace BamTools;
using namespace std;
int main(int argc, char *argv[])
{
    vector<string> inBAM;
    BamMultiReader reader;
    string ifh = string(argv[1]);
    inBAM.push_back(ifh);
    if (!reader.Open(inBAM)){
            cerr << "ERROR: " << ifh << " could not be opened!" << endl;
            return 1;
    }
    BamAlignment al;
    const int start=14990508; // This is the first position in my sample given mpileup (converted to 0 base)
    const int end=15118428; // This is the last position in my sample given mpileup
    double cov=0;
    int nreads=0;
    vector<int> lens;
    while (reader.GetNextAlignmentCore(al)){
            if(al.MapQuality < 10 || al.IsDuplicate()==true || al.IsFailedQC()==true || al.IsMapped()==false || al.IsPrimaryAlignment()==false)
            { continue; }
            int rlen=0;
            vector<CigarOp> cigar = al.CigarData;
            for(vector<CigarOp>::iterator it= cigar.begin(); it != cigar.end(); ++it)
            {
                    if (it->Type == 'M' || it->Type == '=' || it->Type== 'X') {
                            rlen+=it->Length;
                    }
            }
            if(rlen!=0){ ++nreads; }
            lens.push_back(rlen);
    }
    float avg = accumulate (lens.begin(),lens.end(), 0.0)/ lens.size();
    cov = (nreads*avg)/(end-start);
    cout << "NREADS: " << nreads << " AVG_READLEN: " << avg << " RANGE: " << end-start << endl;
    cout << cov << endl;
    return 0;
}

Here's the output

NREADS: 354 AVG_READLEN: 3073.54 RANGE: 127920 8.50557

Here's my samtools mpileup command

 samtools mpileup -A -B -q 10 -Q 0 test.bam | cut -f 4 >tmp

And when I take the average of tmp it's 9.52

Initially before I included some of the flags for mpileup that you recommended I got a value of 4.5X. So this is closer to what mpileup reports

Not sure as to why I'm getting different results.

Edit: samtools depth

I forgot about samtools depth. It's a strong tool.

samtools depth -a -r 1:14990509-15118429 -q 0 -Q 10 test.bam | cut -f 3 >tmp1

The mean of tmp1 is

8.51

Which is the same as the C++ code. So solved! Thanks for helping me learn C++.