Seeing as symbolic math tools are very common nowadays, how acceptable is it to skip calculations in manuscripts?

It's always been normal not to write out long but straightforward calculations in a scientific paper. If there are certain intermediate steps in the calculation that are of interest for their own sake, show them.

will it be frowned upon, even if I specify which software I use and even provide code?

If the calculation is something that can be straightforwardly (but tediously) verified by anyone with knowledge of the field, then I don't see any point in saying what software you used or supplying source code. The reason to give this type of information would be if there was something in the software that could be nontrivial, controversial, etc., so that other people with knowledge of the state of the art might not get the same answer you did.

Do not write out the long boring calculation in a middle of an exposition devoted to a different idea. That makes reading harder. But do present the calculations somehow, e.g., delegate them to a separate section/appendix/supplementary material. Extremely often I found that calculations that I find trivial aren't for others, and sometimes that is because they are wrong.

I am in a very different field as yours - Computational Fluid Dynamics - but the use of external software in simulations is common. In general, a mention of the software and a reference to its documentation or source code if available is given. Providing the mathematical procedure is not necessary since you did not develop it yourself.

The access to a given article and the attached references, and not the article alone as mentioned by others, should enable the reader to reproduce the results.

This is how it usually is presented::

The computation of the cost Function was done using the Tensor Flow toolkit. The reader is referred to [ref] for more details.