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What is the best software if I want to plot an interval, say $[0,+\infty) \times[5,10]\subset\mathbb{R}^2$? Preferably freely available. Of course I could do this with Desmos, LaTeX, or even Excel - but all of them seem quite inconvenient. I know Mathematica is probably the best but unfortunately I don't have access to it.

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I will recommend GeoGebra Classic, it is FREE and joins graphing, geometry, 3D, spreadsheets, computer algebra and probability in one easy-to-use and powerful package.

Figure. In input field type this: $x >= 0 \quad \&\& \quad 5 <= y <= 10$ enter image description here

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Also Wolfram Alpha : x >=0, 5 <= y <= 10 gives this picture:

enter image description here

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