How many plays and poems did Shakespeare write?
We're not exactly sure. We think there are two lost Shakespeares, Cardenio and Love's Labour's Won. Some scholars think that Shakespeare wrote Edward III alone, and we know he had a share in writing Sir Thomas More. Some other plays - like Henry VIII (included in the usual total) - are thought to have been co-written with other writers. The Two Noble Kinsmen, though not included in the First Folio, is also now generally believed to be by Shakespeare.
So the answer to "how many plays?" depends on who you believe. It's 38 (including "The Two Noble Kinsmen") Edward III and Sir Thomas More, and - if they indeed existed - Cardenio and Love's Labour's Won. That comes to 42.
Poems is a similar story, I think. We know what we've got: 154 sonnets, A Lover's Complaint, The Rape of Lucrece, Venus and Adonis, The Phoenix and the Turtle, and The Passionate Pilgrim. Though again some scholars disagree about precisely which ones are wholly Shakespeare.
So the jury's out. The lack of information points to the lack of information we have about Shakespeare himself.