f(x) := x^2 + 3

Defines a simple function f(x) that returns x² + 3.

sum(n) :=
    Prog
        s ← 0
        for i ∈ 1..n
            s ← s + i
        return s

Uses a program block to sum integers from 1 to n.

g(x) :=
    if x < 0
        -x
    otherwise
        x

Implements a conditional function using if-otherwise.

y(x) := sin(x)
Dy(x) := d/dx(y(x))

Computes a derivative using Mathcad’s built-in derivative operator.

A :=
    ⎡1 2 3⎤
    ⎣4 5 6⎦
    ⎣7 8 9⎦

Creates a 3×3 matrix using indexed assignment.

Simpson(f, a, b, n) :=
    Prog
        h ← (b - a)/n
        s ← f(a) + f(b)
        for i ∈ 1..n-1
            if mod(i,2)=0
                s ← s + 2*f(a+i*h)
            otherwise
                s ← s + 4*f(a+i*h)
        return s*h/3

Uses a program block to perform Simpson’s rule numerical integration.

Given
    x + y = 10
    x*y = 21
Find(x, y)

Solves two equations using the Mathcad solve block.

vec(n) :=
    Prog
        v ← zeros(n)
        for i ∈ 1..n
            v[i ← i^2
        return v

Builds a vector y where y[i] = i² inside a program loop.

h(x) := x*exp(-x) - 0.1
x0 := root(h(x), x)

Uses root function to find solution of an equation.

Newton(f, df, x0, n) :=
    Prog
        x ← x0
        for i ∈ 1..n
            x ← x - f(x)/df(x)
        return x

Uses a loop to approximate a root using Newton's method.