\documentclass{article}
\usepackage{latexml}
\usepackage{amsmath}
\lxDeclare[role=ID]{$a$}
\lxDeclare[role=ID]{$b$}
\lxDeclare[role=ID]{$\Phi$}
\lxDeclare[role=ID]{$\Psi$}
\lxDeclare[role=ID]{$\mathcal{H}$}
\lxDeclare[role=FUNCTION]{$F$}
\begin{document}
\[ a+b \]
\[ F(a) \]
\[ \frac{1}{(1+a_0)} \]
\[ \int_a^b F(x) dx \]
\[ a+F(a,b) \]
\[ F(a,b) \]
\[ F(a) + \binom{a}{b} \]
\[ \left\langle\Psi\middle|\mathcal{H}\middle|\Phi\right\rangle 
  +  \defint{a}{b}{F(x)}{x} \]
\[ \baddefint{a}{b}{F(x)}{x} \]
\[ \binom{F(a)}{a+b} \]
\end{document}