Learn English – Difference between “function” and “operation”

I worked at a library. Depending on the job, librarian could still fit, even if the person did not have a specialized degree.

M-W defines librarian as:

a specialist in the care or management of a library

The key term here is 'specialist'. People who serve a specialized role in the library, like doing research or managing a department, would commonly be called librarians. Similarly, the head of a school library would also be a librarian, regardless of their degree.

Someone like me, whose primary job was to put books back on the shelves and man the check out desk, would more commonly be called a library assistant or simply library staff.

In that context I'd use “...after another”, as it suggests a sequence of throws. By contrast, the “...after the other” form suggests (to me) exactly two throws, rather than some number from one to eight throws. A useful comparison of terms similar to consecutive in macmillandictionary says that “one after another” indicates little time between things, which I think is sometimes true but not always. For example, the “one after another” entry at dictionary.cambridge.org says “many, in a series” and makes no mention of rate.

The form “One X after another” refers to a series of X's; as in, eg, One Monster After Another, or in Arnold Toynbee's comment about “the dogma that History is just 'one damned thing after another....'”.