How did Daniel in the lions' den die?

The Book of Daniel says that Daniel was captured in the 3rd year of the reign of Jehoiakim. On this evidence, Daniel must have been in captivity 70 years by the time the Persians defeated the Babylonians. Daniel would probably have been in his late seventies or early eighties by the time the Book says that he was thrown in the lion's den.

However, the Book of Daniel says that the Persian king, who defeated the Babylonians and later attempted to sacrifice Daniel to the lions, was Darius. But historians say that Cyrus was the Persian king who defeated the Babylonians, and that Darius was a successor. If the author really intended to place this event during the actual reign of Darius, then Daniel would have been at least ninety and possibly more than 100 years old at the time.