How To Use The Mathematics Calculation Software Maple (part 2)

How to use the mathematics calculation software Maple (part 2)

In the first part, we have discussed what the software can do,  install the software step by step, and some basic knowledge of the function. Today, on the second and final installment of this 2 part guide, I will guide you on using Maple to solve some basic algebra problems that are most commonly seen in high school.

From part 1 of this article, you have learned that there are 5 areas to work in Maple and to solve these algebra problems, we will need to work in the Math area. If you are in the Text area, you will have to choose the symbol before typing in the commands.

As you can see, there is a brown > before each command you type in.

Let’s solve the equations as below:

a) x^2 + 2x + 1 = 0

b) x^3 + 2x + 3 + 4 =0

You can either type the commands manually or use the Expression card to enter the formulas in. This is especially handy when you are new to the program and are not yet familiar with the commands.

Note: In cases where you need to solve multiple problems on a single work page, you will need to put before each problem the command

Restart to avoid a problem using results from the previous one, leading to problems calculating or even wrong answers.


  • After each command ending with “;”  the result will give it back and show on the screen. If you don’t want the result to be printed, use  :
  • If you don’t know how to use a certain command on Maple, you can put a ? before the command and then press Enter, and the Maple Help window will pop up with a description and example of that command in use.


Operations and mathematics signs

For every command, I will show both the syntax and its meaning (except for the simple ones like + for plus, etc.)

Operations and signs for Maple are similar to the ones used in Pascal. Maple has a total of 12 Operations and signs.


Syntax Meaning
! Factorial
^ Exponentiation
+ Plus
Minus or negative number
* Multiply
/ Divide
< Less than
> Greater than
>= Greater or equal to
<= Less or equal to
= Equal to
:= Assignment


Some common functions in Maple


Syntax Meaning
Sin, cos, tan, cot Trigonometric functions
Arcsin, arccos, arctan, arccot Reverse trigonometric functions
abs Absolute function
exp Exponentiation with exponent e
ln Logarithm function with logarithmic base e
log Logarithm function
sqrt Square root

Some common constant values


Syntax Constant value
Pi π
exp e

Arithmetic operations in Maple

Basic arithmetic operations

The four basic operations

  • Plus: 1+1;
  • Minus: 7-6;
  • Multiply 3*2;
  • Divide: 7/3;


  • 3^2;
  • 3^5;

Square root

  • sqrt(125)
  • sqrt(100)
  • 5*5^(½)

Order of operations

By default, Maple will first do Exponentiation, then Squareroot, followed by Multiply, Divide, and then Plus, and Minus.

To put a certain operation as a priority, you will need to put in brackets ()

  • 4+6/2;
  • 10/(2^3+4);

Operations with integer

1.    Lowest common multiple (LCM) of 2 or more integers

  • To find the LCM of 2 integers a and b, we use the command lcm(a,b) ;
  • To find the LCM of 3 integers a, b and c, we use lcm(lcm(a,b),c);

2.    Greatest common divisor (GCD)

  • To find the GCD of 2 integers a and b, we use GCD(a,b);
  • To find the GCD of 3 integers a, b and c, we use GCD(GCD(a,b),c);

3.    Analyze an integer to its prime number factors

  • To analyze integer a to its prime number factors, we use isprime(a);

4.    Finding a prime number before or after an integer

  • To find the prime number before integer a, we use prevprime(a);
  • To find the prime number after integer a, we use nextprime(a);

5.    Finding integer solution to a problem or equations

  • To find an integer solution to a problem, we use isolve(problem,{parameters});
  • To find an integer solution to an equation we use isolve(problem 1, problem 2,…, {parameters});

6.    Finding quotient or remainder of a division

  • To find the quotient of the operation a divided by b, we use iquo(a,b);
  • To find the remainder of the operation a divided by b we use irem(a,b);

7.    Solving a module problem

  • To solve a problem with module p in Z we use msolve(problem, p);
  • To solve an equation with module p in Z we use msolve({problem 1, problem 2,…}, p);

Operations with decimal numbers

1.    Calculate the approximation of an expression

  • To calculate the approximate value of an expression to the 6th decimal, we use evalf(expression, k);

2.    Simplifying an expression

  • To simplify expression f, we use simplify(f)

3.    Finding the greatest/lowest number in a string of numbers

  • To find the greatest/lowest number in a string of numbers a, b, c,… we use max(a, b, c,…); or min(a, b, c,…);

4.    Finding the maximum/minimum value of an expression

  • To find the maximum/minimum value of an expression, we use maximize(expression, range); or minimize(expression, range);

 Note: If the range is R, you don’t need to type in the Range

5.    Solving a problem or an equation

  • To solve a problem or an equation we use isolve(problem, variable); or isolve({problem 1, problem 2,…}, {variable 1, variable 2,…});

 Note: Sometimes, Maple will show the solution in the form of commands like RoofOf. To get an explicit answer, you need to add the command _EnExplicit:=true

Operations with polynomial

1.    Plus, minus, multiply, divide polynomial

The commands for plus, minus, multiply, divide for polynomial are the same as for integers. We only need to note a few things :

  • Between the coefficient and the variable, there needs to be a *. For example, if you want to type 5x, you will have to type 5*x
  • You may need to run the operation multiple times to get the explicit answer.

2.    Simplifying a polynomial

  • To simplify polynomial f, we use simplify(f);

3.    Expanding a polynomial

  • To expand polynomial f, we use expand(f);

4.    Finding remainders and quotient of the division of 2 polynomials

  • To find the quotient of the division between polynomial f and g, we use quo(f, g, x);
  • To find the remainder of the division between polynomial f and g, we use rem(f, g, x);

 5.    Find the value of a polynomial at a variable value

  • To find the value of polynomial f when x=k(t), we use subs(x=k(t), f);

6.    Analyze a polynomial into factors

  • To analyze polynomial f into factors, we use factor(f);

7.    Finding the coefficient of a polynomial

  • To find the coefficient x^n in polynomial f, we use coeff(f, x, n);

8.    Finding a polynomial’s degree

  • To find polynomial f’s degree, we use degree(f, x);

9.    Sort a polynomial’s coefficient under exponent sum

  • To sort polynomial f’s coefficient under exponent sum, we use collect(f, x);

10.  Sort a polynomial in ascending exponent order

  • To sort polynomial f in ascending exponent order, we use sort(f, x, ascending);

11.  Sort a polynomial in descending exponent order

  • To sort polynomial f in descending exponent order, we use sort(f, x, descending);

Function graph

To draw function graph y=f(x) with x in range [a,b] we use plot(f(x), x=a..b);


To draw function graph z=f(x,y) in 3D space with x in range [a,b] and y in range [c,d] we use plot3d(f(x), x=a..b, y=c..d);

plot3d(xy, y=0..1)


Mathematics analysis

Calculating limits

To calculate expression f’s limit, we use limit(f, x=a, ch);


  • f: expression
  • x: variable to choose the limit
  • a is the limit point
  • ch could be one of four: left, right, real, complex

Calculating derivative

  • To calculate an expression’s derivative, we use diff(f, x1, x2,…, xn)


  • f: expression
  • x1, x2,… being variables

Calculating definite integrals and indefinite integrals

  •  To calculate indefinite integrals, we use int(expression, x);
  • To calculate definite integrals, we use int(expression, x=a..b,…);

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