let's say I buy a ticket on UA's website and it's charged in euros or Japanese
yen. UA takes that amount and converts it to USD for the purpose of figuring
out how many award miles I get for that flight.

what exchange rate does UA use?

is it the exchange rate on the day I paid for the ticket on UA's website, or the
day that the flight actually occurs, or the day the miles are posted to my acct?