Conversation so far:
When did Utada Hikaru try the international market?
Her first singles compilation album Utada Hikaru Single Collection Vol.
1 was released on March 31, 2004.
Was it popular?
It became the best-selling album of 2004 in Japan.
Was it popular in worldwide or was this still before she went international?
CANNOTANSWER.
Did she leave Japan during this time?
In mid-2004, Utada moved back to New York.
What did she do there?
began work on a new recording contract with Island Def Jam Music Group.
Did she make and albums or songs with them?
On October 5, 2004, she released her North American English-language debut album, Exodus, under the name "Utada.
Was this popular too?
Exodus became Utada's fourth consecutive release to debut at number 1 and boast 500,000 copies in its first-week sales in Japan.
Was this popular in the US where she made it?
American sales were not as successful, it reached number 160 in the US Billboard 200 chart.
Were there any singles released from this album?
"Easy Breezy" was released as the lead single in early August 2004.

Question: Did she do anything else noteworthy during this time?
Self-contained rewrite: Did Utada Hikaru do anything else noteworthy besides the album Exodus during 2004-05?