Question: Problem with peak positions

I have written a code which generates a Gaussian like curve as a set of points and have written some basic commands to find several important quantities from the plot. The three of importance here are the peak position, peak height and Full Width at Half Maximum.

See the attached minimal working example maple worksheet.

It can find the peak position and the peak height no problem, but another quantity I want it to find is the Full Width at Half Maximum (FWHM). I use the aforementioned calculated values to find the left and right components of the FWHM but the fsolve command just hangs.

In the worksheet this is not evident but in the much longer full code which I run through the terminal and prints the values to a file, it begins the fsolve command and reaches a particular value and it just hangs. No amount of waiting time makes it continue the calculation.

However if I use an approximate integration scheme (such as Riemann sums) then the fsolve part executed perfectly. fslove seems to get stuck during the numerical integration step.

There is probably an easy answer to this problem which I am missing. Any help is appreciated.

fsolve_numerical_integration.mw

- Yeti