@Kitonum thank you 

@tomleslie 

thanks, i needed it because it is sometimes asked from us to give the results in a specific way.
thanks for your help

@Carl Love 
 thanks, it s working now.
I m using an old version of maple (5)

@Preben Alsholm 

Thank you.

how to change it so that the imput is the differential equation?

the dsolve is not working, it said dsolve needs 2 arguments...

can you please help me with this? 

@Kitonum 

Thanks very much Kitonum

@Carl Love 

that is what I have done :

restart:
 xold:=1.5:
 f:=x->tan(x)-x-1:
 divis:= subs(x=xold,f(x))/subs(x=xold,diff(f(x),x)):
 xnew:=xold-divis:
 dp:=7:
 while xnew-xold>5.0*10.0^(-(dp+1)) do
 xnew:=xold:
 od;
 xnew;

@Carl Love 

Thanks , you were really very helpful

@Carl Love 

Thanks.
you are right, I need to study assembly language or maybe something even lower level. But I find it more difficult and challenging than just using already defined procedures. 

the thing is: I just started a degree in maths, and sometimes the prof requires that... anyhow thanks very much for your help :) 

@Kitonum 

thanks for your answer,
the thing is, I need to write that procedure without the use of any other maple procedures.

@mehdi jafari 

Thanks very much :~)

@Carl Love 

Thanks @Carl Love


(( Why do you want to write this procedure? to learn programming? to learn about Maple? to learn about primes?-->
I wanted to do this to learn programming and about maple as I just started studying at the university :) )