How to curve text within a paragraph text block that is a predefined shape.

Does anyone know how to curve text within a shape, as paragraph text, not artistic text? (See my attached image.)
 

I have drawn the shape, inserted the text as paragraph text, but the text always wants to sit straight.  I am so frustrated as I can find a workaround in either Corel or Adobe CS products.  I have tried using artictic text in Corel, but have to do it line by line - and this brings other problems, such as I cant justify each line with each other, and sometimes a character jumps up relative to the other characters and the entire paragraph does not taper in...so this is not a solution, apart from the fact it will take me FOREVER to insert line by line....I would like to treat the text as a multiple line paragraph, and follow the shape. 

So, to all you brilliant designers out there....PLEASE HELP! 

Thanx!