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Mathematica
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Mathematica as a Calculator
You can use Mathematica just like a calculator: you type in questions, and Mathematica prints back answers.
Ask Mathematica what 3 + 5 is; it prints back 8. Mathematica adds the In and Out labels; you do not type them. You end each line with 

.
The ^ stands for "to the power of".
This asks Mathematica to work out the inverse of a 2 x 2 matrix.
Mathematica can handle formulas as well as numbers.
This asks Mathematica to integrate a simple function.
This asks Mathematica to solve a quadratic equation. The result is a list of rules for x convenient for use in other calculations.
Mathematica can also create two and three-dimensional graphics.
This creates a 2D plot of a simple function.
Here is a 3D plot.
You can access many of the calculator features of Mathematica just by pushing buttons in standard palettes.
Learn more about palettes