"Arigato gozaimasu" is a polite and formal expression of gratitude. It is used in most situations, both formal and informal, but especially when speaking to someone older than you, someone in a position of authority, or someone you don't know well.
"Arigato gozai mashi tai" doesn't exist as a proper Japanese phrase. It seems to be a combination of "arigato gozaimasu" and a conjugation that doesn't fit the context.
If you are trying to express something like "I want to thank you," you would say:
* "Arigato gozaimasu": This would be the most common and natural way to express this. It conveys the feeling of wanting to thank someone.
* "Dōmo arigatō gozaimasu": This is a slightly more emphatic way of saying "thank you" and is often used when you are feeling particularly grateful.
It's important to note that the nuances of Japanese politeness can be complex, and it's best to use the correct phrasing for the situation.