1\documentclass{article}
2\usepackage{latexml}
3\usepackage{amsmath}
4\lxDeclare[role=ID]{$a$}
5\lxDeclare[role=ID]{$b$}
6\lxDeclare[role=ID]{$\Phi$}
7\lxDeclare[role=ID]{$\Psi$}
8\lxDeclare[role=ID]{$\mathcal{H}$}
9\lxDeclare[role=FUNCTION]{$F$}
10\begin{document}
11\[ a+b \]
12\[ F(a) \]
13\[ \frac{1}{(1+a_0)} \]
14\[ \int_a^b F(x) dx \]
15\[ a+F(a,b) \]
16\[ F(a,b) \]
17\[ F(a) + \binom{a}{b} \]
18\[ \left\langle\Psi\middle|\mathcal{H}\middle|\Phi\right\rangle
19  +  \defint{a}{b}{F(x)}{x} \]
20\[ \baddefint{a}{b}{F(x)}{x} \]
21\[ \binom{F(a)}{a+b} \]
22\end{document}