request for help getting maxima to plot the like i would want

Hello everybody,

I have been using and developing linux for 3 years and am an experienced 
user. I am following some basic mathematical classes on my university. 
In this collage I have to use software to calculate and analyze 
functions. The software that is used is called Derive:
http://en.wikipedia.org/wiki/Derive_computer_algebra_system

For a real FLOSS user this is not an option, so I went trying out all 
the mathematical tools for GNU/Linux. I think maxima is the program that 
should be able to do all the calculations and visualisations on the 
functions I use. However after spending a day working and trying I cant 
get my functions to plot the way I want and to calculate on them 
(differentiations / Integration / Compare / Solve).

I tried to do somethings but its not working out very well.

Would somebody be willing to help me out, and demonstrate the command 
required to be able to plot in almost exactly the same way as the 2 
example pages with the plots, that I included as attachment.

Kind regards,

Jelle


Formulas and things i was working on:

f(z):=-x-y+5;
f(z):=9-x^2-Y^2;
f(z):=5-x^2;

f(z):=-2*x-y+4;
f(z):=-x-3*y+6;
f(z):=x+y-4;

f(z):=x^2+y^2=r^2;
r:3;

f(z0):=0=y-x^2;
f(z1):=1=y-x^2;
f(z4):=4=y-x^2;

solve(f(z0));

f(z):=5-x^2;
plot2d(f(z),[x,-6,6],[y,-6,6],[xlabel,"X"],[ylabel,"Y"],[gnuplot_preamble,"set 
xzeroaxis;set yzeroaxis;unset border;set xtics"]);


plot3d(f(z),[x,-6,6],[y,-6,6]);
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