\documentclass{article}
\usepackage{amsmath}
\usepackage{amsopn}
\usepackage{latexml}
\lxDeclare[role=ID]{$a$}%
\lxDeclare[role=ID]{$b$}%
\lxDeclare[role=ID]{$c$}%
\lxDeclare[role=ID]{$d$}%
\lxDeclare[role=ID]{$e$}%
\lxDeclare[role=FUNCTION]{$f$}%
\lxDeclare[role=FUNCTION]{$g$}%
\lxDeclare[role=FUNCTION]{$h$}%
\lxDeclare[role=OPERATOR]{$D$}%
\lxDeclare[role=OPERATOR]{$G$}%
\lxDeclare[role=OPERATOR]{$H$}%

\DeclareMathOperator{\diffd}{\operatorname{d}\!}
\begin{document}

\section{Integration and Summation}
\[ \sum_{a=0}^\infty f_a(c^a) \]
\[ \sum_{a=0}^\infty \sum_{b=-a}^a f_a(c^a) g_b(c^b) \]
\[ \sum_{a=0}^\infty \sum_{b=-a}^a \lim_{c\rightarrow 0} f_a(c^a) g_b(c^b) \]

\[ \int_a^b f(x) dx \]
\[ \int_a^b f(x) \diffd x \]
\[ \diffd u = \diffd x + \diffd y \]

\section{Operators}
\[  D a \]
\[  D f \]
\[  D f(a) \]
\[  D G H f \]
\[  D G H f (a) \]
\[  D (a) (b) \]
\[ D -1 \]

\section{Higher constructs}
% pseudo-differential operator over a function f
\[ |\nabla|^{\alpha} f \]

\section{Logic operators}
\[ \exists x . P(x) \]

\end{document}
