This app was mentioned in
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Archimedes Calculator was newly made available for free. Previously it was something like $ 4.
It's slick, no ads, requires no permissions, slightly basic, but still has functions for trigonometry, logarithms of base n, n-th root, n-th powers and can solve equations.
It also displays division as fractions, making input look just like what you would do on paper.
What are your favorite calculator apps?
I use these -