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The error message you are seeing means that the integrand for the NIntegrate statement has a variable in it. If you would like to nest numeric functions like this, please consider using ?NumericQ as shown in this tutorial:

http://support.wolfram.com/kb/3820. Additionally, if you are doing a double integral, NIntegrate is capable of handling those as well. For example:

(*A double integral*)

NIntegrate[Sin[x y], {x, 0, 10}, {y, 0, 1}]

Note that if we want to use functions like you did, the following will usually not work and at least give warning messages for the reasons mentioned in the tutorial:

myFunction [y_] := NIntegrate[Sin[x y], {x, 0, 10}]

NIntegrate[myFunction[y], {y, 0, 1}]

Use ?NumericQ to delay the evaluation of myFunction until y is given a numeric value:

Clear[myFunction];

myFunction [y_?NumericQ] := NIntegrate[Sin[x y], {x, 0, 10}]

NIntegrate[myFunction[y], {y, 0, 1}]