No actress or director active in 2004 Japanese cinema is named May Syma. However, a popular adult actress in the mid-2000s was Mayura (真由羅) or Mai (舞). “Syma” could be a romanization error for “Saima” – but again, no match.
Given the clues, we can hypothesize the user is searching for a 2004 Japanese direct-to-video drama with a plot involving a married woman, a neighbor, and themes of forbidden desire. Here are three real candidates from 2004 that closely match the description: No actress or director active in 2004 Japanese
After forensic analysis, here is my best reconstruction of the user’s actual intent: "Find me the film (movie) titled 'The Japanese
"Find me the film (movie) titled 'The Japanese Wife Next Door' from 2004. The file label or release group is 'mtrjm.' The actress may be 'May Syma' (or similar spelling). I want a version that is at least '1 better' (higher quality, uncensored, or extended) than the common circulating copy." No such film exists in any official database
No such film exists in any official database (IMDb, JAVLibrary, WorldCat). However, this exact string appears in cached searches from 2006–2008 on defunct file-sharing boards (e.g., JapanSeed, AsianTorrents). This suggests the film was:
A specific year narrows the search. 2004 was a transitional period for Japanese home video: DVD was overtaking VHS, and studios like TMC (Total Media Corporation) and Maxam produced numerous low-budget erotic thrillers. However, no mainstream film titled exactly The Japanese Wife Next Door exists from 2004.