I used to use Siri all the time to ask it (for example) “How much is $1,254 U.S. dollars in Japanese yen?”
It would also answer using the current exchange rate.
Now it tends to give me replies like this. Not very useful.
Do you always get that? I’m asking because I just tried the exact query you specified and it worked as expected for me. Perhaps it’s due to some transient issue?
UPDATE: I realized that I’m not saying “U.S. Dollars.” When I say simple “dollars” I get the exchange rate. If I say “U.S. Dollars” I get a web search as you showed.
Not always. I just tried it a bunch of times, just saying “dollars” and it worked many times. But it seems like at a certain amount it starts switching to some search results.
How high can you go? 
When I say “Hey Siri, Convert one-thousand two-hundred and fifty-four U S Dollars to Japanese Yen” it works as expected and reports the actual conversion not the rate.
If I leave out the “U S” it still works fine.
How high can you go?
Do you mean maximum dollars or are you meaning how high is your voice when you ask Siri?
Maximum dollars.