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I download and unzip to my own directory and use the command prompt on Windows installations.
What "MySQL prompt" are you referring to? I've never used the Windows Installer (executable) version myself, so if you used that to install I would not be familiar with any bundled tools.
mysqldump --user=something --password=something some db > db.sql;
mysqldump --user=something --password=something some db > db.sql;
Is not an internal mysql command. Mysqldump is an external program, although I've never tried it while in mysql, it should be executed after exiting mysql. If this is the problem, it may mean mysqldump installed on your local computer but not the server.