I find it a lot easier to think about e.g. integration as int(a, b, f(x), x) rather than $\int_{a}^{b}{f(x)}dx$. And even addition seems more intuitive as add(a,b) rather than $a+b$.
Is there a term for thinking like that or is this just being weird with notation?
Placing the name of the function first is called "Prefix notation" also referred to as "polish notation". It's the notation used by the programming language lisp.