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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?

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    As far as the basic binary operations go, this is a lot like [Polish notation](https://en.wikipedia.org/wiki/Polish_notation) – 2017-01-16
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    Although not quite what you mention, operational calculus is a very useful, and sadly neglected way of treating calculus operators in an algebraic way. – 2017-01-16
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    @alb I'd love to see a refrence for operational calculus. – 2017-01-16
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    @QthePlatypus wiki has a page: https://en.wikipedia.org/wiki/Operational_calculus. I'm currently reading https://www.amazon.com/Transforms-Applications-Differential-Equations-Mathematics/dp/0486788113/ref=pd_sbs_14_t_1?_encoding=UTF8&psc=1&refRID=B22CE7ZW3HP17RT5T6FS, which is a good exposition of the classical theory (Laplace Transform sends ODEs to algebraic equations). – 2017-01-17

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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.