Some of the Basic Maple commands;

1)	Algebraic Expressions

Numerical vs. Algebraic Expressions:
	> 5 / 7;
	> evalf ( 5 / 7);     # Numerical evaluation of 5/7
	> sqrt(3), Pi;
	> evalf ( Pi, 40 );     # Numerical value of Pi with 40 digits of accuarcy

Object Oriented Assignments:
	> y := 4*x - 3;
	> y^2 + 5*x + 3;    # Output is (4x - 3)^2 + 5x + 3
	> subs ( x = t, y );      # Output is  4t - 3
	> eqn1 := 4*x + 3 = x + 7;     # The name of the equation is eqn1
	> y := lhs ( eqn1 );
	> z := rhs ( eqn1 );
	> eqn2 := y - z = 0;     # This is equivalent to the following two equations
	> eqn3 := " +  ( 4 = 4 );     # Output is  3x = 4
	> eqn4 := " / 3;     # Output is x = 4/3
	> isolate ( eqn2, x );    # Output is x = 4/3
	> solve ( eqn1, x );     # Output is x = 4/3
	> subs (eqn4, eqn1 );     # Output is 25/3 = 25/3

Assignments as Functions:
	> f := (x) -> sqrt ( 9 - x^2 );
	> g := (x) -> x - 5;
	> (f+g)(x), (f/g)(x), (f@g)(x), (f@g@f)(x)
	>
	> h := proc ( x )
	> if 0 <= x and x <=3 then
	>	x^2
	> else
	>	ERROR ( x, `Not in Domain`)
	> fi
	> end:
	> h(0), h(2);     # Output 0, 4
	> h(4);     # Output  Error, (in h) 4, Not in Domain
	>
	> k := proc ( x )     # piecewise defined function with nested if statements
	> if -3 <= x and x <= 3 then
	>	x^2 - 2
	> elif 3 < x and x <= 5 then
	>	x - 3
	> elif x > 5 then
	>	-x^2 + 34
	> elif
	>	undefined
	> fi
	> end:
	> plot (k, -10 .. 10 );
	> Q := series ( sin (x), x=0, 10 );     # Tenth deg. Taylor polynomial \
	>                                                   expansion about x=0
	> P := convert ( Q, polynom );     # Create an output as a normal polynomial
	> P_as_function_of_x := makeproc ( P, x );     # Define as a function \
	>     The procedure 'makeproc' have to be 'student[makeproc]' on some editions
	> plot(P_as_function_of_x(x), x = -1 .. 1);
	> P_as_function_of_x ( 1 );

Some Calculus Commands
	> Limit ( f(x), x = a, right );     # Echo the right hand limit expression
	> limit ( f(x), x = a, right );     # Find the right hand limit
	> diff ( f(x), x );     # The first derivative of f(x) w.r.t. x
	> diff ( f(x), x, x );     # The second derivative of f(x) w.r.t. x
	> showtangent ( f(x), t = 0, t = -1 .. 1 );     # Show the tangent line and the /
	>     graph
	> convert(1.5, rational);     # Change 1.5 to 3/2
	> slope ( [a, f(a)], [b, f(b)] );     # The slope of the line through points
	> vertical( [a, 0], [a, f(a)] );     # Draw a vertical line from/to
Some notes about the plotting an object
	Sometimes you might run into an error when mixing objects. The following is a
	problem I ran into last semester in my DE class. The question is an initial value
	problem.

	> de := diff(y(x), x) = (x - y(x))/(1+x^2+y(x)^2):
	> ic := y(0) = 1:
	> result := dsolve( {de, ic}, y(x), numeric):
	> result(0);     # Output is a list(vector) [x = 0, y(x) = 1.]
	> result(0) [2];     # This isolates the second component, i.e. y(x) = 1
	> # I was trying to use the answer resulted from 'dsolve' command as a function,
	> # but I could not isolate the second component of the result as a function. So
	> # I tried,
	> result(x);     # ERROR, this does NOT work
	> 
	> # To define the solution y(x) which is the second part of result(x), we need
	> # to define a procedure as follows;
	>
	> myproc := proc ( t )
	>	local t, j, k:
	>	k := result(t):
	>	j := nops ( k ):
	>	for i from 1 to j do
	>		if ( convert(lhs( op(ik k) ), string ) = `y(x)` ) then
	>			RETURN ( rsh(op(i, k) ) )
	>		fi
	>	od:
	> end: # The end of this procedure
	>
	>plot ( 'myproc(x)', x = 0 .. 3 );