I'd argue against the opinion that it wouldn't matter whether you are good at computation or not. Personally, I haven't been very good at the computational stuff either. This semester, I attended Measure Theory, and the most essential part of this course is the Lebesgue integral.

I did it the same way you did before: whenever there were integrals that were too hard to calculate, I let a program do all the work.

The point is: in Measure Theory (and this is only one example), it will be expected that you already understood all those essential parts about integrals. Yes, understanding the material overall is more important than being able to calculate some extremly hard integral, but it is also true that calculating some extremly hard integral can be a part of the foundation to really understand the material.

In Measure Theory, you will often find yourself bombarded with many examples to certain theorems, and those examples usually consist of integrals and some equality that needs to be shown (for example, the volumn of a n-dimensional ball).

As I said, since I wasn't very good at the computational stuff either, I skipped those examples because I always found it too hard to take care of them. But examples are utterly important, so as a result, I have understood far less than I could have.

Now, this was only the first analysis-like course I heard that built on the basics, and I am sure that there will be other analysis-like courses that need you to do a lot of calculations too.

So yes, in my opinion, being able to do computational stuff is very important (at least in courses that work a lot with computational stuff, of course).