Is there a function $f(A)$ or $f(Z, A)$ that gets the energy of nuclear binding of one nuclide in atom? Or other way to get it? My chemistry book says only to get it from the chart which is very impractical.
Nuclear physics is very complicated and full of unsolved problems. For example, we seem to understand rather poorly the effects of three-body forces between nucleons, and describing them quantitatively is probably out of the question. Therefore, I expect that nuclei binding energies for most isotopes are solely determined empirically and have no good theoretical curve to originate from. Maybe there are statistically fitted curves to the data we have, though they may well not have a simple form and likely are only good approximations for relatively small intervals.
Edit: As it turns out, equations indeed exist, though as expected they are quite unwieldy and are semi-empirical.
I hope to be not wrong, but believe recalling this to be one of the holy grails in theoretical nuclear physics and a testing benchmark for most comprehensive [field] theories on that subject.
A given theory's proper prediction of binding energies/ masses is also a pre requirement towards the concept of a Theory of Everything - should it even be feasible.
I remember as an undergrad having been fascinated for months on end by the obscure Heim theory, trying to approach its mathematics. It took me a while to un-glamour myself and realize that it is virtually impossible for a theory so old and unaccepted to be as good as its advocates state. Statistically speaking, there is always a chance that you can derive at magical results with a lucky mixture of the right constants and formulas. But these new constants would then need to reveal meaning in other natural concepts as well, in order to make sense in the first place.
I don't know much of the status quo, but I would surmise deriving the binding energies is still a matter of more or less competing theories, each with successes in their own right, but none covering the entire chemical elemental spectrum solely based on fundamental physical constants.
As I recall there are several semi-empirical formulas. Nicolau Saker Neto, already pointed out one.