If you don’t say “the algebra,” “the trigonometry,” “the geometry,” or even “the mathematics.” I see no reason to say “the calculus.”
In the cases where you do use those forms (“The algebra involved in this problem”), I see no problem with using the “the calculus” construction.
Math/Physics major checking in…
To me “The Calculus” refers to a complete set of calculations and algorithms invented in support of explaining a set of physical problems.
What we learn in “Calculus 101” is a subset of that, and rarely for the purpose of the sort understanding that Newton (and I presume Leibniz) were after. Otherwise, the math courses and the intro physics courses would be taught as one, and might very well be called “The Calculus 101” and “The Calculus 102” etc.
But maybe that is just my sense of things, it was a long time ago…
No, Newton called differentials fluxions, which is the reason for the last poll choice. According to the wiki article, he called integrals “fluents” (which I did not know).