Gauss-Cronrod has week point with periodical function.
Please check out following article;
This is in Japanese, so you are OK, but for anyone else please use Google translation.
Unfortunately all numerical integration approximations have some weak points, especially when there are discontinuities or even periodicity, that's why it's required to do some prior analysis of the function to be numerically integrated, In the case of periodic functions it's possible to limit the integration to the area of one period (keeping in mind any change of sign) and then multiply the result by the number of periods.
In my tests Gauss-Kronrod Quadrature is the most robust algorithm for almost every situation and that's probably the reason TI and Casio are using it. I will try to post a Romberg algorithm version tomorrow, Romberg has been traditionally used by HP and it works well for any well-behaved function but not as robust as Gauss-Kronrod in some tricky situations.