Even without resorting to external tools the expression register(:h @=) can act as a surprisingly good builtin calculator, and there is a moderately large builtin math library(:h functions).

Like all registers you can abuse it in many ways too, like as dirty inplace calculator when you're writing docs. For example, yank a example calculation, insert from register(:h i_CTRL-R_=), operate on your yank(:h @").

But are those functionality available natively without plugins? All these are in the default emacs distribution possibly since more than 20 years, and are in a very usable, stable state of functionality.

Aren't these technically plugins for emacs that are shipped with the editor? Org-mode is a plugin for emacs too right?

Sure but what’s the difference? That’s the beauty (and occasional curse) of Emacs. There’s no hard line between “native” code and plugins, outside of the Emacs Lisp interpreter.

Exactly. Its the basically same way with vim. Some plugins are distributed with the editor and some are not

Some of them do take plugins (the netrw plugin I think) but this plugin is included and active in a default install.